In this article, an accurate Chebyshev finite spectral method for the 2-D extended Boussinesq equations is proposed. The method combines the advantages of both the finite difference and spectral methods. The Adams-Bashforth predictor and the fourth-order Adams-Moulton corrector are adopted for the numerical solution of the governing differential equations. An efficient wave absorption strategy is also proposed to effectively absorb waves at outgoing wave boundaries and reflected waves from the interior of the computational domain due to barriers and bottom slopes at the incident wave boundary to avoid contamination of the specified incident wave conditions. The proposed method is verified by a case where experimental data are available for comparison for both regular and irregular waves. The case is wave diffraction over a shoal reported by Vincent and Briggs. Numerical results agree very well with the corresponding experimental data.