In this paper, an efficient numerical simulation solver for pulsed eddy current testing (PECT) signals was developed, and based on this the quantitative non-destructive testing of local wall thinning defect in pipes of nuclear power plants (NPPs) was conducted. First, a frequency domain summation method combined with interpolation strategy was proposed and implemented based on finite element method with edge element for the PECT simulation. Comparison of numerical results and experimental results verified the efficiency of the developed simulation solver for PECT signals. Second, a self-differential probe which can penetrate deeper was proposed to detect the subsurface local wall thinning defect in pipe walls of NPPs. Through analyzing the simulation results calculated using the developed simulator, it was found that the distance between the positive peak and the negative peak of the Bz (magnetic flux density in z direction) in scanning signals can be considered as a feature to quantify the width of defect, while the minimum time to peak of the differential Bx (magnetic flux density in x direction) can quantify the depth of defect.