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

Partial regularity of suitable weak solutions of the Navier-Stokes-Planck-Nernst-Poisson equation