This work based on a new numerical scheme for the numerical solutions of the Chen–Lee–Liu equation using Haar wavelet collocation method. In this work, we combined the backward Euler difference (BED) formula with the Haar wavelet collocation method (HWCM). The BED formula approximates the time derivative of the Chen–Lee–Liu equation, while the HWCM approximates the space derivatives of the Chen–Lee–Liu equation, consequently converting it into a finite system of algebraic equations. Furthermore, we validate the accuracy of the proposed method numerically and graphically with the help of several examples. Moreover, we have also presented an error analysis to prove the convergence of the proposed method.