In a mean-field approximation, we study the in-medium effective potential of the two-flavor quark meson model in the presence of a fermionic vacuum term at a finite temperature and density. There exists a crossover phase transition in the low-density region, and also there is a first-order phase transition in the high-density region accompanied by a critical end point. For the first-order phase transition, when the temperature is close to the critical temperature, the values of surface tension are calculated at various chemical potentials and we find that our results are very close to the results recently found in other chiral models with two flavors. Some consequences and possible applications of our results are also pointed out for the experiments on heavy ion collisions and the evolutions of the compact stars in their early stages.