The House voted, 367 to 13, last night to curtail government regulation of the nation's trucking industry.

Like airline and banking deregulation bills already enacted into law, and a rail deregulation bill that is pending, the trucking bill is designed to introduce more competition into a heavily regulated sector of the economy.

The measure would make it easier for new trucking companies to enter the business and for existing companies to expand their services, give them more freedom to raise or lower freight rates without government intervention, gradually limit the anti-trust immunity that enables competing trucking firms to agree on prices they will charge and pave the way for elimination of many routes and commodity restrictions that inhibit fuel-saving and efficient operations.

In a statement released by the White House last night, President Carter praised the House for taking a major step in the fight against inflation. "By increasing competition and ending irrational regulatory restrictions, the bill will save shippers and consumers billions of dollars each year and conserve hundreds of millions of gallons of fuel," Carter said.

Darius W. Gaskins Jr., chairman of the Interstate Commerce Commission, called the legislation balanced and comprehensive reform. "Shippers, consumers and the trucking industry can expect swift action by the commission to implement this bill with its new congressional emphasis on increased competition," Gaskins said.

Although the House bill does not go nearly as far toward deregulation as does the Senate-passed measure, Senate acquiescence in the House version is virtually assured, and the bill could be on President Carter's desk before he returns from Europe next week.

The House measure was a compromise worked out by key committee members, the bill's sponsors in the Senate and the administration.

Sens. Howard W. Cannon (D-Nev.) and Bob Packwood (R-Ore.), the bill's chief Senate sponsors, earlier had agreed to recommend accepting the House version without a conference if the bill were not weakened on the House floor.

During lengthy debate yesterday, the House rejected several attempts to alter the bill substantively. It defeated:

By 192 to 189, an attempt by Rep. Elliott H. Levitas (D-Ga.) to impose a modified one-house veto on regulations by the Interstate Commerce Commission. Under his amendment, an ICC regulation would have been effective 90 days after promulgation unless both houses had passed resolutions of disapproval or one house had adopted such a resolution and the other chamber did not defeat it.

By 287 to 113, an amendment by Rep. Millicent Fenwick (R-N.J.) to exempt all food products from federal truck regulation. The Senate measure contains this provision.

By 338 to 57, another Levitas-sponsored motion, an attempt to delete a provision that its backers said could reduce food costs. Under the provision, sellers of food and grocery items who use a uniform zone delivered pricing system could give buyers using their own trucks to pick up the products a discount amounting to the cost of the transportation. Currently, sellers give an allowance that is the average of the transportation costs for all buyers in the zone, no matter how close or far away they are from the warehouse.

Although the House version would not reduce trucking regulations as much as desired by deregulation proponents including President Carter and Sen. Edward M. Kennedy (D-Mass.), it retains most of the important elements they advocated.

It would significantly lower barriers to entry into the industry by making it easier for trucking companies to obtain operating certificates from the ICC.

The ICC would be required to grant an application from a firm that showed fitness and evidence of a useful public purpose for the proposed service. The application could be turned down only if opponents could prove that granting it would be inconsistent with the public convenience and necessity.

The House bill also would establish a schedule for removal of restrictions that now prohibit companies from carrying certain commodities or stopping at certain cities or traveling the most direct routes.

The bill also would eliminate -- beginning in 1984 -- authority of rate bureaus to discuss or vote on single-line rates. These cover shipments that a company picks up and delivers without transferring the goods to another company. Also, rates established under the bill's zone of rate freedom could not be set collectively.