The hot jet injection is utilized to actively control the oblique detonation wave, such as initiating and stabilizing an oblique detonation wave at a desired position that is shorter than the length of induction zone, and adjust the height of the oblique detonation wave at the exit of com-bustor when the oblique detonation wave engine is working on off-design flight conditions. The fifth order Weighted Essentially Non-Oscillatory (WENO) scheme and a two-step reversible reaction mechanism of the stoichiometric H2/Air are adopted in the simulations. With the help of hot jet injection, the transition from inert oblique shock wave to the oblique detonation wave immediately occurs near the position of hot jet injection, and consequently the length of combustor can be reduced. The angle of oblique detonation wave also decreases as the hot jet injection approaches the nose of wedge. Additionally, the height of the oblique detonation wave at the exit of combustor can be flexibly adjusted, and also depends on the injection position and the strength of the hot jet. If the velocity of the hot jet is too weak to directly trigger the overall oblique detonation wave at the position of injection, increasing the injection pressure will improve the strength of the hot jet and results in a successful transition.