Marriott Corp., the Bethesda-based hotel, restaurant and entertainment conglomerate, reported yesterday the best quarter in the company's 51-year history.

For the third quarter ended Sept. 7, Marriott's net income was $24.9 million, up 27 percent over the third quarter of 1978, which was also a record. Earnings per share were 70 cents, up from 51 cents in the third quarter of 1978.

Marriott explained that the rate of gain for net income was less than for earnings per share because of a company stock repurchase program. The effect of the program was to reduce the number of shares outstanding and increase interest expense.

Sales for the third quarter were $396.3 million, a 19 percent increase over the same period a year earlier.

President J. W. Marriott Jr. said: "All groups are ahead of last year, with the hotel, contract food services and theme park groups showing substantial improvements."

Marriott Hotels enjoyed a 27 percent increase in profits over the third quarter of a year ago. "Advance bookings are at record levels despite all reports about a recession," Marriott added.

Food services jumped by 29 percent, mainly because of a substantial increase in airline traffic and the addition of new airline accounts, the company said.

The theme parks had the best summer season in their four years of operations, with the combined profits of parks near Chicago and San Francisco up 47 percent over the third quarter of 1978.

Marriott said that per capita spending at the parks rose to more than $16, a record amount.

Restaurant operations increased profits by 7.5 percent over the third quarter of 1978, even in the face of a declining number of customers, a malady that has been troubling the restaurant industry at large, Marriott said.

Marriott's Roy Rogers fast food division was "off slightly," although units in greater Washington D.C. -- the division's largest fast food market -- held their own," the company reported.

Sun Line, which operates cruise ships in the Mediterranean and Aegean, enjoyed somewhat improved profits, despite increased fuel costs, Marriott said.

As for the balance of the year, J. W. Marriott Jr. predicted that "some restaurant business may remain sluggish the rest of 1979, but other operations expect more good results. This will be an outstanding year."