Hechinger Co. said yesterday it plans to sell up to 1.4 million shares of new stock to the public to finance a recently announced acceleration of the Washington home center chain's expansion.

The offering statement calls for the company itself to sell 600,000 shares and for another 675,000 shares to be sold by affiliates of the Hechinger and England families, which control the firm. Another 127,500 shares could be sold if the offer is oversubscribed.

The stock to be sold represents a little more than 9 percent of the 13.7 million shares that Hechinger has outstanding.

The stock sale would leave the offspring of founder Sidney Hechinger in firm control of the rapidly growing retail chain, but would boost the amount of Hechinger stock controlled by public investors from 35 percent to 42.5 percent of the company.

No offering price for the new shares has been set, but the offering would raise nearly $30 million at the current price of Hechinger shares, which closed yesterday at $23.50 in the over-the-counter market.

The sale of 600,000 shares by the company itself would provide additional cash for the ambitious expansion plan announced last week by Hechinger. The 34-store chain said it will open seven more outlets this year and seven more in 1984. A cluster of four stores in North Carolina and several additional units in the Philadelphia area are scheduled.

Though it will cost the company about $1.6 million to open each of the new stores, Hechinger has cash remaining from a stock offering two years ago that could provide much of that financing.

Only last month, Hechinger completed a three-for-two stock split that substantially boosted the number of shares available for trading.

The new stock will be sold sometime this spring after the registration statement has been approved by the Securities and Exchange Commission. The Merrill Lynch White Weld Capital Markets Group in New York will be the underwriter of the issue.

Besides the stock to be sold from the company's treasury, Hechinger shares will be offered by two trusts and two partnerships controlled by Hechinger family memberships. The John W. Hechinger family trust and the Richard England family trusts each plan to sell 112,500 shares.