Because of the mass density-dependence, an extra term should be added to the expression of pressure. However, it should not appear in that of energy according to both the general ensemble theory and basic thermodynamic principle. We give a detail derivation of the thermodynamics with density-dependent particle masses. With our recently determined quark mass scaling, we study strange quark matter in this new thermodynamic treatment, which still indicates a possible absolute stability as previously found. However, the density behavior of the sound velocity is opposite to the previous finding, but consistent with one of our recent publication. We have also studied the structure of strange stars using the obtained equation of state.

6 pages, 6 PS figures, REVTeX style