Line clipping is one of the fundamental problems in computer graphics. In this paper, two well known algorithms are analyzed and a new algorithm, which simplifies the line clipping into the processes in two basic cases by doing simple transformation on two end points of a line in turn, is introduced. The algorithm effectively overrides the shortcomings existed in the above two algorithms such as too many subroutine calls and complex basic cases. Both theoretic analysis and example testing show that the new algorithm is better than well known algorithms.