Using the empirical tight-binding method, the bond lengths and lattice constants in the GexSi1-x alloys are calculated through minimizing the total energy in zincb-lend-like crystal models, with which the GexSi1-x alloys are simulated. With the tight-binding method the electronic band structures are calculated for the models before and after the atoms relax and the calculated results are compared with that obtained in virtual crystal approximation. The calculated results are as follows: The bond lengths in the GexSi1-x alloys generally do not depend up on the alloy compo-sition and nearly equal to the bond lengths in the Ge and Si crystals respectively. This result is consistent with the experiments quite well. The relaxation of atoms has little effects on the electronic band structures for the alloys. However, the chemical composition disorder plays the most important role in determining them.