<p>This paper introduces a cubic B-spline quasi-interpolation (CBSQI) technique for addressing the nonlinear hyperbolic sine-Gordon equation, which holds significant relevance in fields such as fluxion propagation, metal dislocation, and the quantum Heisenberg model. The aim and motivation behind this study are that quasi interpolants have never been used in solving hyperbolic partial differential equations. The approach involves presenting a numerical scheme that utilizes quasi-interpolation method to effectively estimate the derivatives of the dependent variable in the partial differential equations. The cubic B-spline function has been used for the space-discretization. A finite difference scheme has been applied for the time-discretization of the partial differential equation. Derivatives have been replaced with the quasi interpolation method. The stability of the method has been checked by using the matrix analysis method. The proposed scheme is found to be stable which is favorable for calculating results at higher time levels. The effectiveness of the proposed approach has been validated through four numerical experiments. Computed results have been demonstrated through tables and figures. The obtained results demonstrate satisfactory performance and agree favorably with previous studies.</p>