The optimality system is derived for an optimal control problem governed by a time-fractional PDE. A fully discrete finite element method along with convolution quadrature for time discretization are proposed to determine approximate solutions of the optimality system. Almost optimal convergence of O(tau vertical bar ln tau vertical bar+ h(2)) is proved for the proposed numerical method, relying only on regularity assumptions on the data, without extra assumptions on the regularity of solutions of the optimality system.