<p>A new quadrilateral edge element method is proposed and analyzed for Maxwell equations. This proposed method is based on Duan-Liang quadrilateral element (Math. Comp. 73(2004), pp. 1–18). When applied to the eigenvalue problem, the method is spectral-correct and spurious-free. Stability and error estimates are obtained, including the interpolation error estimates and the error estimates between the finite element solution and the exact solution. The method is suitable for singular solution as well as smooth solution, and consequently, the method is valid for nonconvex domains which may have a number of reentrant corners. Of course, the method is suitable for arbitrary quadrilaterals (under the usual shape-regular condition).</p>