In the work, we consider the zero Mach number limit of compressible primitive equations in the domain R 2 ×2T or T 2 ×2T. We identify the limit equations to be the primitive equations with the incompressible condition. The convergence behaviors are studied in both R^ 2 ×T^2 and T ^2 ×T^2, respectively. This paper takes into account the high oscillating acoustic waves and is an extension of our previous work in [29].