In this paper, a novel scheme, cubic Hyperbolic B-spline-based Differential Quadrature Method, is proposed for the solution of 1D non-linear viscous coupled Burgers' equation. The numerical approximation of this mentioned equation is obtained by using the Hyperbolic B-spline-based Differential quadrature method. Hyperbolic B-spline is used as a basis function in DQM in order to obtain weighting coefficients, then received a set of ODEs is solved by using Strong Stability Preserving Runge Kutta-43 scheme (SSP-RK43 scheme). The accuracy and effectiveness of this proposed scheme are tested by using three examples. The obtained results are matched with the previous results present in the literature of other methods as well as with the exact solutions by means of $L^2$ and $L^\infty$ error norms mainly, in the form of tables and figures, the proposed scheme has produced better results. The analysis of the stability of this proposed scheme is also discussed by means of examples at different grid points, which indicated that the proposed scheme cubic Hyperbolic B-spline-based DQM is unconditionally stable. For the stability of the present scheme, the matrix stability analysis method is used.