The notion of weak solution for stochastic differential equation with terminal conditions is in-troduced. By Girsanov transformation, the equivalence of existence of weak solutions for two-type equationsis established. Several sufficient conditions for the existence of the weak solutions for stochastic differentialequation with terminal conditions are obtained, and the solution existence condition for this type of equations isrelaxed. Finally, an example is given to show that the result is an essential extension of the one under Lipschitzcondition on g with respect to (Y, Z).