The partition function of a double minimum oscillator is evaluated by means of variation perturbation theory. For low temperatures, the method cannot be applied in the usual way. Even for a symmetric double minimum potential VDM(-C), the shift of the harmonic reference oscillator is not always zero as expected, but its minimum is near one of the minima of VDM(^) at low temperatures. The partition function thus calculated is only half the correct value. For sufficiently high temperature, the method works normally. The anomaly in the low temperature region is investigated in detail, and a modification of the variation perturbation method is suggested which eliminates most of the problems.