Suburban Insurance, a subsidiary of Suburban Bank, plans to offer a full line of business and family insurance at four of the Maryland bank's branch offices starting Oct. 1, the company announced yesterday.

The move is intended to place Suburban in a more competitive position with the New York money-center banks entering the state, as well as with local discount insurance companies, officials said. Citibank and Chase Manhattan are creating a presence in Maryland as a result of changes in interstate banking laws.

Perpetual American Bank, with headquarters in Virginia, also has an insurance subsidiary operating in Maryland. Two additional state-chartered banks plan to sell insurance, according to Maryland's banking commissioner. Federally chartered banks are prohibited from selling insurance policies except those directly related to credit, but no such prohibition exists for state-chartered institutions such as Suburban and Perpetual.

Suburban, which acts as an agent for leading underwriters, will market a discounted-premium type of coverage available to qualified auto and home owners at a price it says will meet or be better than prices for similar products now available. Suburban plans to avoid charging service fees on installment payments by debiting customers' checking accounts directly. It also will offer property, casualty, life and health insurance.

Licensed agents will work in Suburban branches in Landover Hills, Rockville, Bethesda and Silver Spring. Four more Suburban branches will begin selling insurance next year. Although operations will be concentrated in Maryland, the agents are licensed to do business in the District and Virginia as well.

Suburban Insurance was founded in 1955 but has not been very active in the intervening years. In 1984, it wrote about $2 million in premiums; this year, it expects to write $5 million. Dennis R. Hanson, Suburban's executive vice president, said the company decided to be more aggressive because of the inevitability of money-center banks entering the insurance business.