This paper provides an convergence analysis of a fractional-step projection method for the controlled-source electromagnetic induction problems in heterogenous electrically conducting media by means of finite element approximations. Error estimates in finite time are given. And it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of (O)(hs + τ) in the L2-norm for the magnetic field H, where h is the mesh size and 1/2 ＜ s ≤ 1.