Molecular dynamic (MD) simulations with new interatomic potential function including the covalent bond were performed on the phase transition of $alpha$-quartz-type GeO2 under high pressure. The optimized crystal structure and the pressure dependence of the lattice constant showed higher reproducibility than the previous models and were in very good agreement with the experimental data. A phase transition of $alpha$-quartz and $alpha$-quartz-type GeO2 by simulation was found approximately 24 GPa and 6-7 GPa, respectively. This phase transition involved an abrupt volume shrinkage and showed 4-6 coordination mixed structure with the increasing in the coordination number of cation.