Abstract: A variational path integral method is presented to calculate the partition function of a quantual dissipative system. Two trial functions for the frequency function of the potential and the slope function of the coupling from factor are determined by minimizing of the effective potential. Thus the final partition function becomes an average value under a Gaussion distribution function. Compared with Monte Carlo method, the results calculated by the variational path integral are more accurate in a wide range of temperature.

Key words: Variational path-integral, Quantual dissipative system, Partition function