  This paper is concerned with the long time behavior of Langevin dynamics of
{\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order
system of Brownian particles driven by an external force and a pairwise
repulsive Coulomb force. We prove that the system converges exponentially to
the unique Boltzmann-Gibbs invariant measure under a weighted total variation
distance. The proof relies on a novel construction of Lyapunov function for the
Coulomb system.
