The investigation of stochastic optimal power flow (SOPF) is to seek the optimal solution of static stability constrained optimal power flow considering the uncertainty of parameters in power systems. To solve the problem, this paper proposes an approach based on the stochastic collocation method (SCM) and Gram-Charlier expansion to obtain the optimal solution of SOPF. Firstly, the SOPF model to simultaneously consider uncertainties and static stability is formulated. Then, probabilistic chance constraints are reformulated as a set of deterministic constraints using polynomial approximation, which explicitly describe the relationship between the probability of chance constraints and control variables. By applying the primal-dual interior point method to the reformulated SOPF model, the optimal solution can be efficiently obtained. The proposed SCM-based approach has been thoroughly tested on a modified 3-machine 9-bus system and IEEE 118-bus system, which verifies the effectiveness and accuracy of the proposed method.