The recently discovered Dirac and Weyl semimetals are new members of topological materials. Starting from them, topological superconductivity may be achieved, e.g., by carrier doping or applying pressure. Here we report high-pressure resistance and X-ray diffraction study of the three-dimensional topological Dirac semimetal Cd3As2. Superconductivity with Tc≈2.0 K is observed at 8.5 GPa. The Tc keeps increasing to about 4.0 K at 21.3 GPa, then shows a nearly constant pressure dependence up to the highest pressure 50.9 GPa. The X-ray diffraction measurements reveal a structure phase transition around 3.5 GPa. Our observation of superconductivity in pressurised topological Dirac semimetal Cd3As2 provides a new candidate for topological superconductor, as argued in a recent point contact study and a theoretical work.