In this project numerical procedures dependent on a relatively new B-spline called the cubic Trigonometric B-spline (CTBS) and the finite difference methods (FDM) for Second order non-classical diffusion problems are presented. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Three problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature