The precise mathematical models of tooth surfaces and fillet surfaces of the hypoid gear are established. Three indexes of average semimajor axis of contact ellipses, the direction angle of contact path and the intersection of the transmission error curve are selected to evaluate the tooth contact pattern and the transmission error. Then, taking a hypoid gear for example, the finite element analysis model of hypoid gears transmission system is established which is suitable for tooth contact characteristics analysis under quasistatic condition. By the analysis of quasistatic motion and loaded tooth contact, the variations of bending stresses, contact stresses, and transmission error are investigated. Besides, the results are compared with the calculated results by empirical formula. Finally, a hypoid gear transmission performance test bed is developed, then the tooth contact pattern test and bending stress test are carried out, and the test results are well consistent with the simulation results.