To reveal the mechanism of deflagration to detonation transition promoted by transverse jet, the flame acceleration and detonation initiation process of H2/Air under transverse jet was numerically investigated. According to the flame propagation characteristics and the main factors that promote flame acceleration in different periods, the process of deflagration to detonation transition was divided into four stages: initial flame development stage, turbulence-flame interaction stage, shock-flame interaction stage, detonation initiation stage. The flame acceleration process of each stage was analyzed in detail. The results indicated that the curling and stretching effect of the transverse jet and vortexes on the flame can effectively increase the flame velocity. The flame would constantly produce compression waves during acceleration. The transverse wave formed by the superposition of the compression waves would be reflected multiple times between the walls and act on the flame front, which is critical for flame acceleration. In addition, the positive feedback between the leading shock wave and the flame was also important for the continuous increase of flame velocity.