Molybdenum (Mo) is a body-centered-cubic (BCC) transition metal that has widespread technological applications. While the BCC transition elements are used as test cases for understanding the behavior of metals under extreme conditions, the melting curves and phase transitions of these elements have been the subject of stark disagreements in recent years. Here we use X-ray diffraction to examine the phase stability and melting behavior of Mo under shock loading to 450 GPa. The BCC phase of Mo remains stable along the Hugoniot until 380 GPa. Our results do not support previous claims of a shallow melting curve for molybdenum.