Abstract: This paper studies the initial-boundary value problem of a class of generalized BBM-KdV equations with homogeneous boundary conditions, and proposes a three-layer linear average implicit finite difference scheme with second-order theoretical accuracy.; A conservation of the problem itself is reasonably simulated. We give a priori estimate of the difference scheme and discuss the existence and uniqueness of its difference decomposition, and use the discrete functional analysis method to prove the convergence and unconditional stability of the scheme. Finally, the reliability of the numerical method is verified by numerical simulation.