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This paper concerns through the numerical treatment of Fisher’s reaction-diffusion equation by using a hybrid numerical method. In this method, the combination of cubic trigonometric B-spline (CTB) base functions and differential quadrature method is used. This reduces the problem to a system of first order ODEs which is solved by “an optimal five stage and fourth-order strong stability preserving Runge-Kutta (SSP-RK54)” scheme. Four examples are considered to compare the present results with exact solutions and the results obtained by existing methods. It is found that the present method is not only quite easy to implement, but also it gives better results than the ones already existing in the literature.