To address the resource-constrained project scheduling problems(RCPSP) involving stochastic task duration, an approximate dynamic programming approach is developed. In this approach, a solution from a deterministic average project is utilised to reduce the computational burden associated with the roll-out policy. The priority rules in this approach are based on the solution from the deterministic problem that is solved once at the beginning of the project. To efficiently obtain feasible solutions for an average project, we utilised the forward-backward relax-and-solve algorithm. The computational results on 1560 standard instances from the well-known PSPLIB show that our approach provides competitive solutions in a short computational time.