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In this paper, we will extend the lattice Boltzmann model (LBM) to deal with the complex coupled nonlinear Schrödinger equations. A D1Q5 nonstandard complex lattice Boltzmann model (CLBM) with amending term for the coupled nonlinear Schrödinger equations (CNLSEs) is proposed. Complex equilibrium distribution functions and amending terms are selected, and the CNLSEs can be recovered by using the Chapman–Enskog multi-scale analysis and Taylor expansion technique. Some initial boundary value problems of the coupled system are simulated to verify the effectiveness and stability of our model. [ABSTRACT FROM AUTHOR]