Assistant Attorney General William Bradford Reynolds, a target of criticism by civil rights leaders, will visit Mississippi next week with black leader Jesse Jackson and a group of civil rights lawyers to look into whether local registration and voting practices discriminate against blacks.

Reynolds, head of the Civil Rights Division, has been criticized repeatedly by civil rights leaders for his opposition to affirmative action quotas and mandatory school busing.

Jackson, who heads Operation PUSH and is considering running for the Democratic presidential nomination, has been promoting a black registration drive in southern states aimed at the 1984 elections.

After meeting with Jackson yesterday, Reynolds said information submitted by Jackson's group "suggests to me there are indeed some serious problems. I've agreed to go down to Mississippi next week and personally look into the complaints."

Jackson said he found a pattern in Mississippi, especially in the heavily black Mississippi Delta area, of requiring voters to register twice, once in their city and once in the county seat.

"Some have to drive 80 or 90 miles to vote," Jackson said, arguing that this is tantamount to a poll tax for a poor person without a car or money for gasoline.

Jackson also complained about "single-shot balloting," which requires a voter to select a slate rather than individual candidates. In addition, he said, Mississippi requires double primaries in multi-candidate races when the leading candidate wins a plurality but not a majority.

He said any black candidate who leads the first primary generally is defeated in the runoff when whites unite behind a white candidate. If Chicago had such a system, the current mayor, Harold Washington, who won the Democratic nomination as a black candidate against two whites who split the white vote, instead would have faced a runoff against former mayor Jane M. Byrne.

Although Mississippi no longer requires literacy tests or poll taxes, Jackson called the state "the slowest and most recalcitrant in moving into full political participation for all its citizens . . . . The new forms of denial are so effective that in the nine southern states not one black congressman has been elected in the 18 years since the Voting Rights Act passed."

Reynolds hopes to deal with Jackson's complaints and with a pending redistricting plan for Mississippi before the state's voter registration deadline July 2. A primary election is scheduled for Aug. 3.

"No redistricting will be allowed to go into effect until the Department of Justice is satisfied that it is in full compliance with the Voting Rights Act and black voters will not be disadvantaged," Reynolds said.

Like other states, Mississippi was required to draw up new election districts after the 1980 census. Under the Voting Rights Act, all Mississippi changes must be approved by the Justice Department to make sure they do not discriminate against minority voters.

In reviewing the plans for county elections to the board of supervisors and the court districts for Mississippi's 82 counties, Justice already has filed objections to one or both for seven counties.

If Reynolds finds violations while he is in Mississippi, he first may ask county officials to change their registration practices. If that fails, he could seek a court order to force the counties to ease registration procedures, or he could send in federal registrars.

Meanwhile, Jackson said, he and other civil rights groups, including the NAACP Legal Defense Fund, the Lawyers' Committee for Civil Rights, Operation PUSH and the Black Bar Association of Mississippi, plan to file suit challenging Mississippi's registration and voting procedures as a violation of both the Constitution and the Voting Rights Act.