The position-dependent effective mass (PDEM) problem is of enormous importance to the realization of the extended Wentzel-Kramers-Brillouin (WKB) approximation in bound state calculations for semiconductor heterostructures. By studying some model problems, we show that the extended WKB method provides good approximations for the bound states with the high eigenenergies. In addition, the effect of the smoothness of the effective mass distribution functions and potential barrier in the PDEM problems is discussed in our work. We found the precision can be affected by the effective mass and potential barrier in the PDEM.