  We develop a superfield formulation of $\mathcal{N}=4$ supersymmetric
Yang-Mills theory with gauged central charge in $USp(4)$ harmonic superspace.
Component formulation of this theory was given by Sohnius, Stelle and West
\cite{SSW80} but its superfield formulation has not been constructed so far. We
construct the superfield action, corresponding to this model, and show that it
reproduces the component action from \cite{SSW80}.
