We introduce the locally-conformal perfectly matched layer (PML) approach, which is an easy and straightforward PML implementation, to the problem of mesh truncation in the finite element method (FEM). This method is based on a locally-defined complex coordinate transformation which has no explicit dependence on the differential geometric characteristics of the PML-free space interface. As a result, it is possible to handle challenging PML geometries with interfaces having arbitrary curvature, especially those with curvature discontinuities. In order to implement this approach, we also introduce the concept of complex space FEM using elements with complex nodal coordinates. After developing the analytical background of this method, we present some numerical results to demonstrate the performance of this method in three-dimensional electromagnetic scattering problems.