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The second order Burger's equation model is used to study the turbulent fluids, suspensions, shock waves, and the propagation of shallow water waves. In the present research, we investigate a numerical solution to the time fractional coupled-Burgers equation (TFCBE) using Crank–Nicolson and the cubic B-spline (CBS) approaches. The time derivative is addressed using Caputo's formula, while the CBS technique with the help of a θ -weighted scheme is utilized to discretize the first- and second-order spatial derivatives. The quasi-linearization technique is used to linearize the non-linear terms. The suggested scheme demonstrates unconditionally stable. Some numerical tests are utilized to evaluate the accuracy and feasibility of the current technique. [ABSTRACT FROM AUTHOR]