In this paper, we employ a reduced basis method for solving the PDE constrained optimization problem governed by a fractional parabolic equation with the fractional derivative in time from order β ∈ (0, 1) is defined by Caputo fractional derivative.Here we use optimize-then-discretize method to solve it. In order to this, First, we extract the optimality conditions for the problem, and then solve them by reduced basis method. To get a numerical technique, the time variable is discretized using a finite difference plan. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution.