In the present work, using a high-resolution three-dimensional numerical analysis the initiation and propagation mechanism of a detonation wave is studied in a circular tube with a hot jet initiation. The reactive Euler equations with a one-step two-species chemistry model are solved based on the structured adaptive mesh refinement technique. Influences of both a single hot jet and impinging double hot jets on the formation of the detonation wave are studied. For each case, the objective is to investigate the role of the tube wall on the initiation and propagation of the detonation wave. The result for both cases shows that the hot jet-induced bow shock forms a complex reflection structure in the circular tube. The reflection effect of the circular wall strengthens the shock and facilitates the formation of the Mach stem, which leads to the formation of the detonation wave. However, when the hot jet condition and the total area of jet hole remain the same, for the case of initiation using double hot jets, the reflection strength of the bow shocks weakens when the diameters of the hot jets become smaller. When using a single hot jet, the initiated detonation is overdriven and propagates in the two-headed mode. In this initiation mode, by increasing the inflow Mach number, a four-headed mode detonation front is formed. While in the case of impinging double hot jets, a four-headed mode detonation front is initiated directly.