An analytic technique, namely the homotopy analysis method, is applied to solve the Navier–Stokes equations governing unsteady viscous flows due to a suddenly stretching surface in a rotating fluid. Unlike perturbation methods, the current approach does not depend upon any small parameters at all. Besides contrary to all other analytic techniques, it provides us with a simple way to ensure the convergence of solution series. In contrast to perturbation approximations which have about 40% average errors for the considered problem, our series solutions agree well with numerical results in the whole time region $0\u2a7dt<+\u221e$. Explicit analytic expressions of the skin friction coefficients are given, which agree well with numerical results in the whole time region $0\u2a7dt<+\u221e$. This analytic approach can be applied to solve some complicated three-dimensional unsteady viscous flows governed by the Navier–Stokes equations.