The densities of liquid NiCoAlCr quaternary alloys with a fixed molar ratio of Ni to Co to Al (x(Ni)-x(Co)-x(Al)≈73-12-15) which is close to the average value of the commercial Ni-based superalloys TMS75, INCO713, CM247LC and CMSX-4, and the mass fraction of chromium changes from 0 to 9% were measured by a modified sessile drop method. It is found that with increasing temperature and chromium concentration in the alloys, the densities of the liquid NiCoAlCr quaternary alloys decrease, whereas the molar volume of the liquid NiCoAlCr quaternary alloys increases. And the liquid densities of NiCoAlCr quaternary alloys calculated from the partial molar volumes of nickel, cobalt, aluminum and chromium in the corresponding Ni-bases binary alloys are in good agreement with the experimental ones, i.e. within the error tolerance range the densities of the liquid Ni-based multi-component alloys can be predicted from the partial volumes of elements in Ni-based binary alloys in liquid state. The molar volume of liquid NiCoAlCr binary alloy shows a negative deviation from the ideal linear mixing and the deviation changes small with the increase of chromium concentration at the same temperature.