Abstract The pricing of American options has been widely acknowledged as “a much more intriguing” problem in financial engineering. In this paper, a “convergency-proved” IFE (inverse finite element) approach is introduced to the field of financial engineering to price American options for the first time. Without involving any linearization process at all, the current approach deals with the nonlinearity of the pricing problem through an “inverse” approach. Numerical results show that the IFE approach is quite accurate and efficient, and can be easily extended to multi-asset or stochastic volatility pricing problems. The key contribution of this paper to the literature is that we have managed to provide a comprehensive convergence analysis for the IFE approach, including not only an error estimate of the adopted discrete scheme but also the convergence of the adopted iterative scheme, which ensures that our numerical solution does indeed converge to the exact one of the original nonlinear system.