Based on Z-scan technique, the nonlinear absorption characteristics and nonlinear refraction characteristics of ZnO crystal, ZnS crystal and ZnSe crystal were studied under the picosecond (ps) laser pulses and the femtosecond (fs) laser pulses respectively. The experimental results show that the nonlinear absorption characteristics of the three kinds of crystals are reverse saturable absorption mainly due to two-photon absorption under the ps laser pulses. The nonlinear refraction characteristics are self-defocusing and the nonlinear refractive indexes are positive because of free carrier. The nonlinear absorption characteristics of the ZnO crystal and ZnS crystal are reverse saturable absorption mainly due to three-photon absorption under the fs laser pulses, and the ZnSe crystal is two-photon absorption. The nonlinear refraction characteristics of the three kinds of crystals are self-focusing because of bound electron. The experimental results show that zinc semiconductor crystals materials and laser pulse width can influence the optical nonlinear characteristics of materials.