The First American Bank of Virginia has filed a $1.1 million suit against direct-mail pioneer Richard A. Viguerie, becoming the latest of a number of creditors who claim the conservative fund-raiser owes them money.

The suit, filed on Monday in Fairfax County Circuit Court, also names as defendants Richlane Enterprises, of which Viguerie is a director, and the Brock Hotel Corp. based in Irving, Tex. Both companies were guarantors on a loan Viguerie obtained from the bank in June 1984 for the purchase of the ShowBiz Pizza Place Restaurant in Fairfax City.

"The First American Bank loaned Mr. Viguerie $1.1 million to finance that ShowBiz Restaurant," said Haynie S. Trotter, attorney for the bank. "It was an installment note, and he was in default."

Viguerie, 52, who lost a bid for the Republican nomination for lieutenant governor last year, did not return a reporter's phone call at his office in Falls Church yesterday.

His attorney, David M. Estabrook, declined to comment. A spokesman for the Brock Hotel Corp., Debra Moore, said the firm had not yet been served with the suit.

The suit filed against Viguerie is the latest sign of financial trouble for Viguerie and the Viguerie Co., the direct-mail organization he owns at 7777 Leesburg Pike in Falls Church.

In March 1985 two conservative political organizations refused to pay Viguerie's company nearly $4 million in disputed fees.

Viguerie is known as the man who originated the idea of raising funds for political candidates through direct mail with one of the largest mailing lists in the country. Though he built an image as a kingmaker in the New Right of the Republican Party, he has been criticized by many of his clients who say that he retains as much as 90 percent of the funds he raises.

Eight suits have been filed in Fairfax Circuit Court against Viguerie and The Viguerie Co. since last May. They are:

*Dec. 6 -- United States Instrument Rentals v. The Viguerie Co., seeking $500,000. The Viguerie Co. consented to the order without admission, court records show. It also agreed to return equipment, including computer software, computer terminals and printers.

*Dec. 6 -- Beacon Printing Co. v. The Viguerie Co. Inc. for goods sold from Jan. 31, 1985, to April 11, 1985, seeking $60,204.99.

*Dec. 11 -- Maryland National Bank v. Richard A. Viguerie seeking $783,395.42 in unpaid principal on a $1 million installment loan.

*Dec. 20 -- Western Union Electronic Mail, v. The Viguerie Co., seeking $18,213.69 for services.

*Sept. 20 -- Empery Corp. v. The Viguerie Co., seeking $70,823.88 for printing services.

*Aug. 29 -- American Paper Products Co. v. The Viguerie Co, seeking $146,514.37 for paper products and materials.

*May 21 -- The Lewis Co. v. The Viguerie Co., seeking $79,223.35 for plastic membership cards and metal litho tabs.

A motion for judgment filed by Western Union Electronic Mail was scheduled to be heard in court today.

The company's attorney, Dwayne L. Garrett, said yesterday that the parties are near agreement and that he will request a one-week continuance.