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We present a parallel algorithm for computing an equilibrium path in a large-scale economic growth model. We exploit the special block structure of the nonlinear systems of equations common in such models. Our algorithm is based on an iterative method of Gauss-Seidel type with prices of different time periods calculated simultaneously rather than recursively. We have implemented the parallel algorithm in OpenMP and MPI programming environments. The numerical results show that speedup improves almost linearly as number of nodes increases. Different methods for solving an individual block: Newton-type methods, Krylov subspace methods and trust-region methods, give similar results for the speedup.