The aim of this paper is to study the CPE (Critical Point Equation) on some paracontact metric manifolds. First, we prove that if a para-Sasakian metric satisfies the CPE, then it is Einstein with constant scalar curvature -2n(2n+1). Next, we prove that if $(\kappa,\mu)$-paracontact metric satisfies the CPE, then it is locally isometric to the product of a flat $(n+1)$-dimensional manifold and $n$-dimensional manifold of negative constant curvature $-4$.