NASHVILLE, Tenn. (AP) _ Hospital Corporation of America's board of directors on Monday approved a $3.6 billion leveraged buyout plan led by senior management, just over a month after rejecting the offer.

The board of the nation's largest health care concern announced late Monday it had agreed to the $51 a share cash and securities offer by TF Investments Inc., a company formed by HCA management and headed by HCA Chairman and Chief Executive Officer Thomas F. Frist Jr.

The group's offer includes $43 in cash and $8 in securities for each of HCA's 71.4 million common shares outstanding.

HCA stock closed up 62 1/2 cents at $46.62 1/2 a share Monday on the New York Stock exchange.

The offer still must be approved by HCA stockholders in a February meeting, company officials stated in a news release. No date was given for the meeting.

Frist could be immediately reached for comment.

A special committee of outside directors had rejected the Frist group's initial offer of $47 a share, and rejected the $51 a share proposal on Oct. 17. The committee at that time indicated it would accept bids from other parties through Nov. 18, although a number of industry analysts expressed skepticism the company would get a higher offer.

''The board's approval was based in part upon the recommendation of a special committee of board comprised of nine outside directors and the opinion of Morgan Stanley that, as of Nov. 21, 1988, the consideration to be paid in the merger is fair to HCA shareholders from a financial point of view,'' according to board's Monday release.

HCA spokesman John Van Mol said he did not know whether any other offers were made by the Nov. 18 deadline.

HCA, which owns or operates nearly 400 hospitals worldwide, set up the special committee to consider buyout offers after the initial proposal in mid- September.

The company sold 104 of its less profitable hospitals just over a year ago to a new employee-owned company, HealthTrust Inc., in a spinoff that netted HCA almost $1.6 billion.