Solution of non-similarity boundary-layer flows over a porous wedge is studied. The free stream velocity U (w) (x) similar to a x (m) and the injection velocity V (w) (x) similar to b x (n) at the surface are considered, which result in the corresponding non-similarity boundary-layer flows governed by a nonlinear partial differential equation. An analytic technique for strongly nonlinear problems, namely, the homotopy analysis method (HAM), is employed to obtain the series solutions of the non-similarity boundary-layer flows over a porous wedge. An auxiliary parameter is introduced to ensure the convergence of solution series. As a result, series solutions valid for all physical parameters in the whole domain are given. Then, the effects of the physical parameters on the skin friction coefficient and displacement thickness are investigated. To the best of our knowledge, it is the first time that the series solutions of this kind of non-similarity boundary-layer flows are reported.