The Justice Department, searching for an alternative to busing, yesterday proposed giving free college education to elementary and high school students who participate in voluntary desegregation.

The department submitted the suggestion to a federal judge in St. Louis who is currently considering that city's nine-year-old school desegregation controversy. The St. Louis Board of Education joined in the proposal.

Under the plan, any black who voluntarily attends the now white suburban schools, and any suburban white who crosses into the city to attend a predominantly black school, would be rewarded with tuition-free attendance at a state institution of higher education, assuming the student can be admitted.

For each year the student attends the "host school," the state would provide one half year of college. Attorney General William French Smith estimated the extra cost to the state at $6 million.

In exchange, "no student would be required to attend any school but that to which he or she would normally be assigned," Smith said. "Every decision concerning the choice of schools and districts would be made by students and their parents."

The department also proposed a less novel system of specialized "magnet" schools in the city and surrounding counties to encourage voluntary enrollment in schools outside the home district.

The St. Louis schools have 63,000 students, about 78 percent of them black. The 23 suburban districts have 150,000 students, of whom 20 percent are black.

St. Louis began court-ordered desegregation within the city last fall. The court is currently considering whether the busing must now cross into the suburbs in order to achieve racial balance.

The proposal, Smith said, "is designed and intended to obviate the necessity of any inter-district mandatory phase of this case."