In this paper the nonlinear absorption in the organic material ZnTBP-CA-PhR is reported. Saturable absorption, reverse saturable absorption and re-reverse saturable absorption under an Ar+ laser beam in visible light range were observed. This material has fine optical limiting properties. Its intensity threshold is lower than that of other materials and there is no nonlinear optical effect before input intensity reaches the threshold. In order to analyse the physical mechanism of nonlinear absorption of this material, a five-level model is presented using the rate equation theory to simulate the saturable absorption and reverse saturable absorption experimental results.