Abstract: We propose the first GPU solution to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight line graph (PSLG) consisting of points and edges. There are many CPU algorithms developed to solve the CDT problem in computational geometry, yet there has been no known prior approach using the parallel computing power of the GPU to solve this problem efficiently. For the special case of the CDT problem with a PSLG consisting of just points, which is the normal Delaunay triangulation problem, a hybrid approach has already been presented that uses the GPU together with the CPU to partially speed up the computation. Our work, on the other hand, accelerates the whole computation by the GPU. Our implementation using the CUDA programming model on NVIDIA GPUs is numerically robust with good speedup, of up to an order of magnitude, compared to the best sequential implementations on the CPU. This result is reflected in our experiment with both randomly generated PSLGs and real world GIS data with millions of points and edges.