During the Depression, Jesse H. Mitchell planted in the center of Washington's black community a bank which over the years helped black businesses sprout and blossom when other financial institutions in the city refused them.

During the 1950s, Mitchell's son, B. Doyle Mitchell, assumed the presidency of the bank, Industrial Bank of Washington. It branched out into three offices and continued to grow with its roots still in the black community.

Yesterday, the younger Mitchell, 65, was selected by the D.C. Bankers Association to a position that will elevate him to president of that association in mid-1982. Mitchell is the first black in Washington ever slated to head the bankers association. He is believed to be the first of 50 black bank presidents in the country to preside over any state-level bankers association.

"He's a good banker. It's not easy to be a banker in today's times," said Thomas Goines, president of the National Bankers Association, the trade association of black-owned banks.

Since Industrial Bank was founded in 1934 by a small group of black businessmen, the D.C. business has stood as a pillar of economic opportunity, the foundation for other aspiring black bankers and the cement to hold together businesses in the black community, particularly when segregation was strong, Washington business people said.

Mitchell's appointment by the D.C. Bankers "signifies a change of attitude and philosophy that used to prevail," said William Fitzgerald, president of the 10-year-old, black-owned Independence Federal Savings and Loan. "Financial institutions for many years were very biased and very racist. Many financial institutions now are integration across the board. But the problem has not been eliminated. I think it's a very positive move they're (D.C. Bankers Association) making."

Some critics of Mitchell, a Howard University graduate who also attended the Wharton School of Finance at the University of Pennsylvania, complained that for many years Industrial catered only to the black elite in Washington before the late 1960s, when the city was not only segregated between blacks and whites but often among blacks themselves.

Not so, said Fitzgerald. Many people who were refused loans by the bank as poor risks were the source of much of the criticism, Fitzgerald said.

"People don't understand financing and banks," Fitzgerald said. "People don't understand the pressure he was under" to make the bank succeed, he said of Mitchell.

"Doyle Mitchell has paid his dues," Fitzgerald continued. "He's the dean of black bankers in this city and perhaps of other banks in this city."

While some praise Mitchell for being a forerunner in black banking, others say he is now slowing his pace and running behind the times.

In the past year, Industrial has been surpassed in the amount of deposits by another, younger black-owned bank here, United National Bank, which is headed by Samuel Foggie, whose banking career started at Industrial during the late 1950s. United opened in 1964.

Foggie, like many newer black bankers, is attempting to expand and continue serving the black community by crossing the color line to attract larger accounts.

Many black-owned banks use advertising to attract new customers but Mitchell does not. Industrial obtains customers "through personal contacts. "Our friends bring in customers," Mitchell said.

Mitchell said that one service his bank provides is the sale of food stamps because many people in the areas where his three offices are lo- cated need them. Some larger D.C. banks recently stopped this service and Mitchell noted that it entails an added cost to the bank that he must offset elsewhere.

Many of Industrial's loans are small consumer loans compared with the more profitable commercial loans upon which other banks rely, Mitchell added. Most of the deposits are small and require more work and higher costs to process.

Mitchell was selected last night to the post of general convention chairman for the bankers' 61st annual convention next summer. Traditionally, the convention head automatically becomes second vice president and then first vice president. At the annual convention in 1982, Mitchell would become the association president if the tradition is followed.