This paper deals with the numerical solution of an axisymmetric transient eddy current problem in a conductive non-linear magnetic media. This means that the relation between the magnetic field and the magnetic induction (i.e., the so-called B-H curve) is non-linear. We analyze a weak formulation of the resulting problem in the axisymmetric case, with the source term given by means of a non-homogeneous Dirichlet boundary condition. For its numerical approximation, we propose a fully discrete scheme based on a finite element method combined with a backward Euler time discretization. We establish its well-posedness and derive error estimates in appropriate norms for the proposed scheme. In particular, we obtain an L-2 rate of convergence of order O (h+Delta t) without assuming any additional regularity of the solution. Moreover, under appropriate smoothness assumptions, we also prove an L-2-like rate of convergence of order O (h(2) + Delta t). Finally, some numerical results, which confirm the theoretically predicted behavior of the method, are reported. (C) 2015 Elsevier Ltd. All rights reserved.