Abstract: In this paper we introduce the notion of weak solution for Backward Stochastic Differential Equation: Y_t=\xi+\int_t^T g\left(s, Y_s, Z_s\right) d s-\int_t^T Z_s d W_s (0.1) By Girsanov transformation, we estabilish the equivalence of existence of weak solutions for equation （0.1） and that of equation: Y_t=\xi+\int_t^T\leftg\left(s, Y_s, Z_s\right)+Z_s \Phi_s\right d s-\int_t^T Z_s d W_s (0.2) The result in 3 is a corollary of this conclusion. We obtain several sufficient conditions for existence of weaksolutions.