An improved neighbor list algorithm is proposed to reduce unnecessary interatomic distance calculations in molecular simulations. It combines the advantages of Verlet table and cell linked list algorithms by using cell decomposition approach to accelerate the neighbor list construction speed, and data sorting method to lower the CPU data cache miss rate, as well as partial updating method to minimize the unnecessary reconstruction of the neighbor list. Both serial and parallel performance of molecular dynamics simulation are evaluated using the proposed algorithm and compared with those using conventional Verlet table and cell linked list algorithms. Results show that the new algorithm outperforms the conventional algorithms by a factor of 2~3 in cases of both small and large number of atoms.