Laser diode (LD) are playing more and more important role in a number of technical areas. However, due to LD's bad beam divergence, researchers have to use sophisticate optical systems to collimate or focus LD into other appliance. It is necessary to collimate laser diode. Whereas if the object is not ideal but with a limited dimension, no matter how to correct the radius, some aberrations may always remain. That is the collimation has a limitation. In this paper, we investigate the limitation for the asymmetric bi-convex lenses by ray tracing method with the help of Femat theory. And obtain the equations which analyze the limitation of the asymmetric bi-convex lenses. By programming the equations, we calculated and the limitation as a function of LD's beam dimension, index and the two radii of curvature of the asymmetric bi-convex lenses respectively. Keeping other conditions invariably and changing LD's beam dimension from 5mm to 150mm with a step of 5mm, we find that the limitation increases approximatively linearly with the increase of the beam dimension. Basing on the results of the calculation, we analyzed and plotted the limitation as a function of index and radii of curvature of the asymmetric bi-convex lenses in detail.