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This paper deals with numerical solution of one dimensional nonlinear sine–Gordon. “Modified cubic B-spline differential quadrature method” is used to solve one dimensional nonlinear sine–Gordon. The method reduces the problem to a system of first order ordinary differential equations (ODEs). The resulting system of ODEs is solved by “an optimal five stage and fourth-order strong stability preserving Runge–Kutta (SSP-RK54) method”. Finally, the method is illustrated and compared with existing methods via numerical examples. It is found that the method not only is quite easy to implement, but also gives better results than the ones already existing in the literature. Keywords: Sine–Gordon equation, MCB-DQM, SSP-RK54, Thomas algorithm