This paper presents how credibility theory and chance constrained optimization method can be efﬁciently applied for modelling and solving transportation problem in fuzzy environment. Since the proposed transportation model includes fuzzy variable coefﬁcients deﬁned through possibility distributions with inﬁnite supports, it is inﬁnite-dimensional optimization problem. Therefore, we can not solve directly it by conventional optimization algorithms. To overcome this difﬁculty, we will discuss the approximation of the fuzzy transportation chance constrained problem in this paper, and design a heuristic algorithm, which combines approximation method (AM), neural network (NN) and genetic algorithm (GA) algorithm to solve this transportation chance constrained model. Finally, we present one numerical example to show the feasibility and effectiveness of the proposed method.