ABSTRACT The goal of this paper is to analyze control properties of the parabolic equation with variable coefficients in the principal part and with a singular inverse-square potential: Here μ is a real constant. It was proved in the paper of Goldstein and Zhang (2003) that the equation is well-posedness when , and in this paper, we mainly consider the case , where are two positive constants which satisfy: . We extend the specific Carleman estimates in the paper of Ervedoza [Control and stabilization properties for a singular heat equation with an inverse-square potential. Commun Partial Differ Equ. 2008;33:1996–2019] and Vancostenoble [Lipschitz stability in inverse source problems for singular parabolic equations. Commun Partial Differ Equ. 2011;36(8):1287–1317] to the system. We obtain that we can control the equation from any non-empty open subset as for the heat equation. Moreover, we will study the case . We consider a sequence of regularized potentials and prove that we cannot stabilize the corresponding systems uniformly with respect to .