Oblique Detonation Wave (ODW) is a key component for hypersonic combustion engines. Its understanding is essential for designing combustors but reliable information on combustion process and exact ODW structure are difficult to obtain. Axisymmetric sharp cones can produce the purest two-dimensional ODW. This study simulates conical ODWs with hypersonic inflow of stoichiometric H2-air at Mach 7.36, using axisymmetric multi-species Laminar Navier-Stokes equations with the Jachimowski and Lutz combustion models. Numerical solutions of inviscid flow, at 40°, 35° and 32° cones, show steady-state overdriven ODW ignited by the pressure coupling of a shock wave and deflagration waves. At 30.5° and 30° cones, the ODWs are near the Chapman-Jouguet (CJ) condition and the coupling occurs between the shock wave and an internal post-shock ODW. The predicted CJ condition is between 30° and 29.5°, with constant detonation angle and minimum entropy being 42.3° and 1864 JkgK . The induction distance is the most sensitive parameter.