Let there be a heap of beans with total number N(odd) and an integer s，we difine a 2-person game Γ(N，s) as follows: The first player P_Ⅰ takes some beans from the heap, at least one bean and at most s beans. Player two，P_II now picks some beans under the same constraint. The play then reverts to P_II and continues in the same way until all beans have been removed. The player with odd number of beans at hand wins. In this paper，We completely solve the game. At first，we give the winning strategy (if exists) for P_Ⅰ. Theorem Let r be the number of beans P_Ⅰ leaving to P_II at any step，and q be the number p_Ⅰ have at the end of the step. Then p_Ⅰ will win if r=1 or 0(mod(2s+2)) if q is odd ,and r=s+1 or s+2(mod(2s+2)) if q is even when s is odd and r=1 or 0 (mod(s+2)) if q is odd,and r=s+1(mod(s+2)) if q is even when s is even. The theorem can be proved by induction. As a by-product of the theorem we have Corollary Γ(n，s) is a win for P_II iff n=S十1 (mod(2s+2)) when s is odd and n=s+1 (mod(s+2)) when s is even.