We investigate the electronic structures and superconductivities of new superconductor MgB2 with different lattice parameters by means of multiple-scattered-Xα calculation. It is shown that the lattice parameters have great effect on the superconductivity of MgB2. The results of this paper show that the density of states at the Fermi level decreases with the decreasing lattice parameters. The effects are very more sensitive substantially to the change of the lattice parameter a as compared with that of the lattice parameter c. Correspondingly,the superconducting transition temperature TC decreases correspondingly mainly with decreasing the lattice parameter a. Our results are in good agreement with the experiments.