This research involves in the development of the spectral collocation method using Bernoulli polynomials to the solution for time fractional convection-diffusion problems arising in groundwater pollution. The main aim is to develop the operational matrices as well as fractional derivative. The advantage of our approach is to orthogonalize the Bernoulli polynomials for sake of creating sparse operational matrices for derivatives in which having one sub diagonal non-zero entries only, andalso creating operational matrix for fractional derivative to obtained the diagonal matrix. Due to these, the convergence of our approach is fast with low cost computations. Discussion on the error analysis for the presented approach is given. Two test problems are considered to illustrate the effectiveness and applicability of our method. The maximum absolute error inthe computed solution compare with the existing method in the literature. The comparison shows that our method is more accurate and easy implemented