Phononic crystals (PnCs) are artificially made materials composed of periodically arranged structures capable of manipulating acoustic/elastic wave propagation characteristics. In this paper, an improved fast plane wave expansion method (IFPWEM) is developed to obtain the band structures of PnCs. In the method presented, the continuity of the algorithm has been improved by eliminating the jump discontinuity points as well as decreasing the number of wave vectors used. Implementing these changes results in increased computational efficiency when compared to the traditional fast plane wave expansion method (FPWEM). In order to increase the band gap width produced by the PnCs, an adaptive genetic algorithm is adopted to optimize the PnCs structural topology for in-plane wave mode (xy mode). The numerical results yielded from optimization of two-dimension (2D) PnCs with a symmetric square lattice microstructure verifies that the efficiency of the IFPWEM is significantly greater than the conventional FPWEM and finite element methods. •AGA-IFPWEM is proposed for topology optimization of PnCs.•IFPWEM is introduced to analyze the band structures of PnCs.•Wave vectors for band structure analysis decrease from 625 to 81 by IFPWEM.•AGA significantly decreases the iterative times required for convergence.