In this paper, an efficient forward numerical simulation solver for pulsed eddy current testing (PECT) signals has been proposed and developed based on the Fourier series method combined with an interpolation strategy and the database approach. Initially, the PECT signal simulation method based on the Fourier series scheme and an interpolation approach is described. Second, the database type fast numerical solver for single frequency ECT problem is introduced to the Fourier-series-based PECT simulation to enhance its simulation efficiency. In addition, an inversion algorithm of PECT has also been proposed and validated, based on the developed efficient simulator of PECT signals and a deterministic optimization strategy, for the profile reconstruction of wall thinning in pipes of nuclear power plants (NPPs). Through inverse analysis using the simulated PECT signals and signals with random noise, the efficiency and the robustness of the proposed PECT inversion algorithm have been demonstrated.