Ab initio calculations of the melting curve of molybdenum for the pressure range 0-400 GPa are reported. The calculations employ density functional theory (DFT) with the Perdew-Burke-Ernzerhof exchange-correlation functional in the projector augmented wave (PAW) implementation. Tests are presented showing that these techniques accurately reproduce experimental data on low-temperature body-centered cubic (bcc) Mo, and that PAW agrees closely with results from the full-potential linearized augmented plane-wave implementation. The work attempts to overcome the uncertainties inherent in earlier DFT calculations of the melting curve of Mo, by using the "reference coexistence" technique to determine the melting curve. In this technique, an empirical reference model (here, the embedded-atom model) is accurately fitted to DFT molecular dynamics data on the liquid and the high-temperature solid, the melting curve of the reference model is determined by simulations of coexisting solid and liquid, and the ab initio melting curve is obtained by applying free-energy corrections. The calculated melting curve agrees well with experiment at ambient pressure and is consistent with shock data at high pressure, but does not agree with the high-pressure melting curve deduced from static compression experiments. Calculated results for the radial distribution function show that the short-range atomic order of the liquid is very similar to that of the high-T solid, with a slight decrease of coordination number on passing from solid to liquid. The electronic densities of states in the two phases show only small differences. The results do not support a recent theory according to which very low dT(m)dP values are expected for bcc transition metals because of electron redistribution between s-p and d states.