Compared with the conventional finite element method that relies on an underlying mesh and element-node connectivity to describe the geometry, meshless method shows its advantage in mesh simplification, tight crack representation and re-meshing process. An effective numerical implementation of the meshless method uses the Galerkin technique and is referred to as the element-free Galerkin (EFG) method. In this paper, the EFG method is applied to a field of electromagnetic computation, namely, simulation of pulsed eddy current testing. The model is validated against analytical solutions.