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In this paper, an improved adaptive fault estimation algorithm is proposed for a class of polytopic linear parameter varying (LPV) systems. The conventional adaptive fault estimation design method suffers from low performance of the fault estimation and a strict equation constrain, so a novel fast adaptive fault estimation (FAFE) design method proposed in this paper not only enhances the performance of fault estimation evidently, but also avoids the strict equation constraint using inequality transform. Furthermore, based on Lyapunov stability theory, new sufficient conditions are given to guarantee the stability of error dynamics in terms of matrix inequalities. Finally, simulation results of a helicopter flight control system are presented to show the effectiveness of the proposed method.