Line clipping against a rectangular window is a fundamental problem in computer graphics. A robust and fast algorithm is needed not only for the traditional graphics pipeline but also for new applications, including web maps, nanomaterials, and sensor measurements. In this paper, we present a novel approach, which is based on the idea of combining the geometric and algebraic approaches. In particular, the proposed approach first decomposes a 2D line clipping problem into a set of 1D clipping problems, and then solves the 1D clipping problem by the comparison (i.e., >, <, and =) operation on the coordinate value of the projected points on one dimension only. Both theoretical analysis and experimental tests were conducted to demonstrate the improved robustness (for degenerated cases) and computational efficiency of the proposed approach.