In this paper, a generalized reaction diffusion equation with delay has been numerically solved by a cubic Bspline Galerkin finite element method. The full discrete numerical process is based on trapezoidal rule. To demonstrate the efficiency of the method, numerical illustrations have been given. Graphs are also displayed in support of the numerical results. Both the theoretical and computational rate of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of numerical scheme is confirmed by computing L2 and L∞ error norms