The purpose of the MAX-SPA-P problem is to establish stable pairs between students and the projects so that the number of matched students is maximum. The MAX-SPA-P problem has been attracting research attention because the theory of stable matching in the MAX-SPA-P problem is widely applied in the fields of education and economics such as finding matching between students and universities, buyers and sellers, suppliers and carriers, etc or any matching problems which have preference list constraints and the maximum number of matchings. So far, several approaches are proposed to solve this problem such as approximation algorithm, min-conflict search, and local search. However, those approaches still have drawbacks in computation time and solution quality for solving the MAX-SPA-P problem of large sizes. This paper presents a new heuristic search to improve performance to solve the MAX-SPA-P problem of large sizes. Our proposed method is to start from a blank matching, we find a maximum stable matching based on Gale-Shapely’s idea by assigning active students to projects which they prefer most on their rank list. If a project or lecturer is over-subscribed, we define a heuristic function for selecting a suitable student to remove from current matching. This assigning process will stop when all students are inactive. The experimental outcomes confirm the better efficiency of our algorithm than both SPA-P-AP and SPA-P-MCH ones based on computation time and solution quality for solving MAX-SPA-P problem of large sizes.