The National Right to Work Committee, noting that it has prevailed in three lawsuits charging the Federal Election Commission with favoritism toward labor unions, launched a campaign yesterday against the reappointment of commission member Thomas E. Harris.

Harris, who was a staff attorney at the AFI-CIO before his appointment to the commission in 1975, will lose his seat April 30 unless President Carter reappoints him.

The Right to Work Committee, a conservative group that describes itself as an opponent of compulsory unionism, said Harris appears to be the most prounion of the commissioners and has thus been one of the chief causes of what the committee calls pro-labor bias in commission decisions.

At a press conference here, the right to work group also called for a congressional investigation of the FEC's rulings on labor matters and said it will use its current suit against the commission to uncover, through discovery proceedings, the relationships between national AFL-CIO political contributions and donations from local unions around the nation.

The election commission administers federal laws limiting the amount of money that individuals and organizations can contribute to candidates in federal elections. A key part of its job is regulating "political action committees," set up by business and labor groups, to assure that the committees do not contribute more than the legal limits.

The Right to Work Committee has charged repeatedly that the FEC enforces the law more vigorously against business than against labor.

U.S. District Court Judge Charles R. Richey agreed with the right to work group in a decision Monday saying that the FEC had no legal basis for its decision to exempt the AFL-CIO from a provision of the federal law designed to prevent groups from evading the contribution limits.

Richey's decision, on a preliminary motion, voids an FEC position that favored the AFL-CIO. Richey will now hold a trial to determine whether or not the AFL-CIO has created a contribution network that violates the law. The Right to Work Committee said it will use discovery proceedings in that suit to dig into the contribution records of the AFL-CIO and its affiliated unions.

Richey's decision marks the third time in two years that the right to work group has prevailed in a legal battle with the FEC.

The group asked the FEC in 1977 to investigate a teachers' union that was using a questionable procedure to raise political money from its members. The commission refused to act; after the right to work group went to court, a federal judge ordered the union to change its procedure and refund to members the political money it has raised.

Next the committee went to court to force the FEC to stop the AFL-CIO from mixing its members' dues money with political contributions. The right to work group won again, and the FEC eventually won an order stopping the union practice. The AFL-CIO paid a $10,000 fine in the case as well.

The FEC and the Right to Work Committee are also suing each other in a fourth action concerning the committee's solicitation methods for its own political contributions.

Harris, the former union officials, and Vernon Thompson, a former Republican officeholder, are both due to lose their seats on the commission on April 30, when their four-year terms expire.

The Right to Work Committee called for the replacement of both commissioners, but it concentrated its fire on Harris.

Congressional aides who follow the commission say Harris has the support of Democratic leaders on Capitol Hill and is likely to be reappointed. Thompson, they say, is less likely to be retained, because GOP leaders have not unanimously supported him for a new term.