2 This paper presents a solution methodology for general formulation of shortest path problem with 3 non-additive continuous convex travel cost functions. The proposed solution methodology is 4 based on outer approximation algorithm which solves the original problem by iterating between 5 the solution of two optimization problems known as subproblem and a master problem. We show 6 that subproblem solution in OA framework for non-additive shortest path problem can be 7 expressed through closed form equations and thus the OA framework can be reduced to solving 8 only the mixed integer linear program of master problem. Numerical experiments conducted on 9 varying size networks based on different combination of nonlinear cost functions show the ability 10 and efficiency of proposed framework in providing the exact global solution. 11 12