New Republican Phil Gramm of Texas won a significant personal victory Saturday night in recapturing the U.S. House seat he abandoned a month ago, but the party victory may have belonged to the Democrats.

Gramm, who quit Congress Jan. 5 and switched parties after his Democratic colleagues knocked him off the House Budget Committee for his cosponsorship and outspoken support of President Reagan's economic program, easily won reelection with 55 percent of the vote against 10 opponents, 9 of them Democrats.

He played down the personal aspect of the victory and said the vote was a mandate to continue the course he has followed in Congress since 1979. Gramm called the mandate "the strongest I have ever received."

"I believe the people of my district said they approve of my work over the past two years," he said in a telephone interview. "They believe we are beginning to see the light at the end of the tunnel and they want us to finish the job."

Gramm, who becomes the first Republican to represent Texas' 6th Congressional District, received congratulatory calls from President Reagan, Vice President Bush and a number of members of Congress.

But Texas Democrats were only temporarily disappointed by the outcome, and several said Gramm appears to be vulnerable if he chooses to run again in the conservative Democratic district in 1984.

Former Texas state representative Dan Kubiak, a Democrat who finished second with 39 percent of the vote, told supporters Saturday night he likely would run again in 1984. "We gave it all we had," he said. "It was a stacked election." Other Democrats are also looking at the race.

The nature of Gramm's personal triumph was most evident from the vote in Brazos County, his home county around Bryan. There he got 66 percent and the 50 percent turnout was the highest in the district.

But Gramm lost six of the rural Democratic counties, and received less than 50 percent of the vote in 11 of the district's 14 counties. He overcame that with overwhelming support in heavily GOP areas north of Houston and south of Dallas.

Despite the party switch, Gramm's advantages in the election were significant. Democrats had only 38 days to field a candidate, raise money and get organized. In addition, Gramm had at least $700,000 at his disposal, while Kubiak raised less than $100,000.

Kubiak was not well known in the district, and relied on existing Democratic organizations to get the vote out for him.

The only other candidate who got more than 1 percent of the vote was humorist John Henry Faulk, who received less than 4 percent.