Princeton University may soon end the policy that limited the number of students who received A’s for their course marks, an approach designed to thwart grade inflation but one that many students cited as the worst part of their Princeton experience.

The current guidelines seek to limit A-range grades to at most 35 percent of the students in each course. The new approach, which the university president, Christopher L. Eisgruber, endorsed in a memorandum on Thursday, would instead encourage individual academic departments to set their own grading standards.

If adopted by the faculty in the fall term, the approach would represent a major shift for the university, which drew widespread attention in 2004 when it first sought to cap grades. At the time, close to 50 percent of Princeton students were getting A-range grades in their classes. The university hoped that other colleges would follow its lead.

That did not happen, which led many Princeton undergraduates to worry that they were entering the job market or applying to graduate schools at a competitive disadvantage. In 2009, when the undergraduate student government conducted a survey that asked students to name their main source of unhappiness, 32 percent cited the grading policy.