We construct a gravity dual of a boost-invariant flow of an SU (N) supersymmetric Yang-Mills gauge theory plasma with chemical potential. We present both a first-order corrected late-time solution in Eddington-Finkelstein coordinates and a zeroth-order solution in parametric form in Fefferman-Graham coordinates. The resulting background takes the form of a time-dependent AdS Reissner-Nordström-type black hole whose horizons move into the bulk of the AdS space. The solution correctly reproduces the energy and charge density as well as the viscosity of the plasma previously computed in the literature.