We study combination of Sinc and B-Spline scaling functions to develop numerical method for the time-fractional convection-diffusion equations. Dou to exponential convergence of Sinc interpolation, the shifted Sinc functions based on double exponential transformation have been used for the spatial discretization, and the B-Spline scaling functions have been used for the temporal discretization. We consider two examples to test the proposed method, and we have compared the presented method to verify the effectiveness of the proposed method in comparison with recent existing methods.