This paper presents a parametric study of an eddy current (EC) sensor that measures the magnetic flux density (MFD) for detecting lack-of-fusion defects commonly found in metal additive manufacturing (Metal-AM). In this study, the EC-sensing system is simulated using a two-stage method that decomposes the EC-based detection of a defective conductor into two subproblems; the first analytically solves for the EC assuming no defects, and the second solves for the EC perturbation in the focused regions near the defects using a distributed current source method. Based on the proposed EC model, the effects of geometrical parameters on the sensitivity of an EC-sensing system were analyzed and verified by comparing with finite-element analysis (FEA). The study leads to the identification of two key parameters that significantly affect the sensitivity and accuracy of an EC sensor for detecting small defects, which are the locations and axes of the MFD sensors relative to the coil. The ECD distributions are simulated for two EC-sensor design scenarios: fixed at specified locations, and scanning over the entire specimen. Both DCS-based and FEA results match excellently well when images are at a fixed senor location. When scanning, DCS-based images are much smoother and require significantly less time to scan as compared to FEA that requires remeshing between steps and exhibits significant numerical noise, demonstrating the accuracy and efficiency of the proposed numerical model.