<p>We consider in this paper numerical approximations for the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system. We propose a decoupled semi-discrete and fully discrete scheme that enjoys the nice properties of positivity preserving, mass conserving, and unconditionally energy stability. Then, we establish the well-posedness and regularity for the initial and (periodic) boundary value problem of the PNP-NS system under suitable assumptions on the initial data, and carry out a rigorous convergence analysis for the fully discretized scheme. We also present some numerical results to validate the positivity preserving property and the accuracy for our decoupled numerical scheme.</p>