Algorithms for line clipping against convex polygon have been studied for a long time and many research papers have been published so far. In spite of the latest graphical hardware development and significant increase of performance the clipping is still a bottleneck of the graphical pipeline. This paper presents a new robust and fast algorithm for line clipping by a convex polygon. The algorithm uses a small pre-processing in order to obtain significant speed up. The proposed algorithm is especially convenient for applications where points or lines are represented in homogeneous coordinates. The algorithm does not use division in floating point representation as the resulting points are in homogeneous coordinates. The algorithms will benefit if vector-vector hardware supported operations can be used.