Assemble nozzles are most widely used in the laser cutting presently, and their resulted jet structure influences laser cutting quality and efficiency remarkably. Based on the axial symmetric N-S equation of compressible liquid, we establish the onflow model to simulate convergent nozzles’ free jet with different internal parameters by using structural grid and finite volume of quadratic precision. The law of the influence of contractive angle of taper nozzles and curvature radius of convergence nozzles’ convergent section on jet structure parameters is revealed, and it can provide a basis for optimization selection and design about laser cutting nozzles.