  In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg
\cite{CKN} on the incompressible Navier-Stokes equation, we establish the
existence of a suitable weak solution to the
Navier-Stokes-Planck-Nernst-Poisson equation in dimension three, which is shown
to be smooth away from a closed set whose $1$-dimensional parabolic Hausdorff
measure is zero.
