There is a large divergence angle of the fast-axis output beam of high power diode laser (HPDL) and the great differences between the fast-axis and slow-axis beam limit the direction application of HPDL. The mathematical model of the LD collimation lens' surface is researched and by using aplanatic principle and considering the position of microlens, two equations of two types of quadratic-vertical surfaces-elliptical surface and hyperbolic surface-are established in a practice way. These two models are simulated in ZEMAX software and the conclusion is elicited; the effect of these two collimation lens are much better than the regular spherical surfaces.