The Langevin equation and the Gaussian average of the stochastic quantization of Parisi and Wu are continued on the closed time-path, at the same time, the new non-Gaussian source is added into it. After assuming some properties of new source, the closed time-path Green functions are computed by using the adapted Langevin equations. While they are transformed into the physical representation, some important characters of closed time-path Green function, i.e. the normalization and causality, are obtained also.