Direct method for Yau filtering system has been studied since 1990s and all these work are limited in time-invariant systems. In this work, we extend the direct method so that it is applicable to time-varying cases. We need less assumptions compared with our previous work. The novelty of this work is that we propose several transformations on the forward Kolmogorov equation so that it can be solved by means of solving some ordinary differential equations if the initial distribution is Gaussian. The corresponding results for any non-Gaussian initial distributions can be obtained via Gaussian approximation. It can be seen that our new scheme direct method can treat nearly most general Yau filtering problems under natural assumptions. Our algorithm has been compared with the extended Kalman filter, multilevel particle filter, and ensemble Kalman filter by numerical examples and the simulation results show the efficiency of our method.