The United States Information Agency has begun a $1 billion modernization of the Voice of America's worldwide radio transmission facilities, including a secret contract that guarantees it use of a privately owned Costa Rican radio station that can broadcast into Nicaragua.

The unusual Costa Rican agreement, under which VOA provides some $3.2 million for the transmission facilities and an annual $168,000 fee to the private association that controls the AM station, circumvents a Costa Rican law that prohibits foreigners from owning broadcast facilities in that country, according to a source close to the San Jose government.

Both sides are bound to keep the agreement's terms secret, according to the source.

The proposed expansion and modernization of VOA's worldwide facilities came as the result of a National Security Council review last year.

It found the agency's transmission facilities "antiquated" and "not capable of maintaining minimum performance levels" in "presenting the U.S. public diplomacy message to the world," according to the fiscal 1985 budget documents sent to Congress this year.

The dramatic growth in VOA's operations -- its budget is up 70 percent since fiscal 1981 -- comes under the directorship of Charles Z. Wick, a close friend of President Reagan.

In a major part of the program, VOA is attempting to negotiate agreements to place $100 million transmitters in unnamed Persian Gulf, Middle Eastern and Far Eastern countries over the next five years to increase substantially the coverage of its shortwave broadcasts beamed into the Soviet Union, according to the agency presentation.

If VOA cannot reach normal government-to-government arrangements, a spokesman said, it will seek agreements with private groups, as was done in Costa Rica.

The agency also is expanding its personnel overseas as a result of the NSC study. VOA bureaus are being opened this year in Geneva, Rome, Islamabad, Hong Kong and Costa Rica.

According to an agency spokesman, "a Polish correspondent" has been hired for the newly established VOA Rome bureau, where the Polish-born Pope John Paul II is a prime source of news directed at Poland.

Next year, VOA plans two new bureaus in Western Europe and two in the United States, increasing its bureaus to 23 overseas and six in this country.

The Costa Rican facility is one part of a $31 million VOA plan to broadcast on AM/FM frequencies, which are easier to pick up than shortwave, in Central America, particularly in Sandinista-controlled Nicaragua.

Late last year, when VOA officials learned they were legally barred from obtaining their own frequency in Costa Rica, they began negotiations with private broad- casters. In December, according to a source close to the Costa Rican government, the private, nonprofit Costa Rican Association for Information and Culture was organized by conservative media executives, journalists and politicians.

On Aug. 30, the day before the agreement was signed between the association and U.S. officials, it was criticized in the Costa Rican congress as a circumvention of the law. However, the signing, which was delayed three times, took place at the home of Costa Rican President Luis Alberto Monge.

A source close to the Costa Rican government said it was at the insistence of U.S. officials. "When a friendly nation asks for something like that, it's very difficult to say no," the source said.

Negotiations have been undertaken to put transmitters in other countries in the region, the VOA spokesman said, adding that until agreements are reached, "they are handled as confidential diplomatic exchanges."

Sources on Capitol Hill said that U.S. Army officers in Honduras this year described another plan to build an AM/FM transmitter in that country that could beam programs south into Nicaragua. These sources said it would be placed on or adjacent to the airfield at San Lorenzo, which U.S. Army engineers have been expanding to handle military exercises and contingency operations.

The Honduras negotiations "are currently on hold," a Reagan administration official said.

Another major element in the Western Hemisphere program is to be a $150 million shortwave and medium-wave relay station in Puerto Rico to cover the Caribbean, Central America and South America. It is projected for completion in August 1990.