In this paper, a class of absolute value equations (AVE) $ Ax-B|Cx| = d $ with $ A, B, C\in \mathbb{R}^{n\times n} $ is considered, which is a generalized form of the published works by Wu ^[1], Wu and Shen ^[2] and Mezzadri ^[3]. Some conditions to guarantee the unique solution of the above AVE are gained. The corresponding results of the above published works are generalized.