By choosing the proper time difference, the algorithmic instability of O(2,4) finite difference time domain (FDTD) method is got rid of in dealing with the crucial distinction of density and elastic constants on interfaces. Using the improved staggered grid FDTD method, we calculated the Г-Х directional band gap of the two-dimensional phononic crystal, which was composed of rectangular arrays of ? 28.5mm steel tubes with lattice constant of 103mm. Calculated results were compared with the measured ones, and both results coincided well.