In the paper we consider a finite-volume approximation for the Cahn-Hilliard equation with dynamic boundary conditions. We prove an error estimate for the fully-discrete scheme. The convergence of the scheme is proved in Nabet (IMA J Numer Anal 36(4): 1898–1942, 2016), we prove here an error estimate for the fully-discrete scheme. We also give numerical simulations which validate the theoretical result.