This paper presents an approach to simultaneously update the velocity and density parameters through full waveform inversion (FWI) in the time domain. A least-square objective function is employed so that both amplitude and phase information are used in the simultaneous inversion. It is well known that the two parameters tend to be highly correlated which results in crosstalk in the inversion. In order to mitigate the crosstalk and balance the updates, the velocity and density gradients are pre-conditioned. A test with the Marmousi II model demonstrates that the simultaneous inversion can reasonably reconstruct the two parameters. The test of a 3D field data indicates that density should be included to reconstruct a reliable velocity model for the improvement of depth migration. Otherwise, the assumption of constant density causes artifacts in the inverted velocity since any seismic data is interpreted in terms of velocity only.