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Recently, many authors have studied the following CH-γ equation:where α 2 , c0 and γ are paramters. Its bounded wave solutions have been investigated mainly for the case α 2 > 0. For the case α 2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the case α 2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.