Context. Modern graphics processing units (GPUs) lead to a major increase in the performance of the computation of astrophysical simulations. Owing to the different nature of GPU architecture compared to traditional central processing units (CPUs) such as x86 architecture, existing numerical codes cannot be easily migrated to run on GPU. Here, we present a new implementation of the numerical method smooth particle hydrodynamics (SPH) using CUDA TM and the first astrophysical application of the new code: the collision between Ceres-sized objects. Aims. The new code allows for a tremendous increase in speed of astrophysical simulations with SPH and self-gravity at low costs for new hardware. Methods. We have implemented the SPH equations to model gas, liquids and elastic, and plastic solid bodies and added a fragmentation model for brittle materials. Self-gravity may be optionally included in the simulations and is treated by the use of a Barnes-Hut tree. Results. We find an impressive performance gain using NVIDIA consumer devices compared to our existing OpenMP code. The new code is freely available to the community upon request.