The pulsed eddy-current testing (PECT) method has the promising capabilities for detecting defects and evaluating material properties. It achieves this through its rich variety of frequency components and large driving electric current. Efficient numerical simulation of PECT signals plays an important role in probe optimization and quantitative signal processing. This study primarily focuses on the development of an efficient numerical solver for PECT signals, and its validation via the consideration of the nondestructive testing problems of wall thinning defects in pipes of nuclear power plants. A frequency domain summation method combined with an interpolation strategy was proposed and implemented. It is based on the finite element method with edge elements. The number of total frequencies used in signal summation and the number of selected frequencies for interpolation were thoroughly discussed. In addition, a code using the time domain integration method was also developed for the signal prediction of a transient PECT problem. It was used for comparison with the frequency domain summation method. A comparison of numerical results of the two proposed simulation methods and experimental results indicates that both of these simulation methods can model PECT signals with high precision. However, the frequency domain summation method combined with an interpolation strategy is much more efficient in its use of simulation time.