<p>The aim of this paper is to present the optimal error estimates for a fully discrete finite element method for the electrohydrodynamics (EHD) model, which couples the Navier-Stokes equations for velocity and pressure with a convection diffusion equation for the charge density and a Poisson equation for the electric potential. The scheme is based on the mixed finite element method for the spatial discretization and the first-order semi-implicit scheme for the temporal discretization. Drawing upon the inherited anti-symmetric structure of the coupling terms in the discrete scheme and the energy argument, optimal error estimates for all variables are provided unconditionally. Numerical results are provided to confirm our theoretical analysis.</p>