We propose to solve a three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Using the axisymmetric assumption, the singular computational domain is reduced to a subset of $\mathbb{R}^{2}$, but the electromagnetic field belong to $\mathbb{R}^{3}$. By performing a Fourier analysis in one dimension, we get a sequence of singular problems set in a 2D domain, and propose a new finite element approach to solve the problem. Numerical experiments illustrate the method.