In inertial confinement fusion facilities, the propagation characteristic of laser quads in the cylindrical hohlraum is especially important for achieving the effective compression of target. In order to understand the irradiation characteristics of laser quads in hohlraum, the propagation model of laser quads in vacuum cylindrical hohlraum for the typical structure and beam configuration has been built up. The propagation characteristics of multiple laser quads have been numerically simulated. Considering the crossing beam energy transfer and laser plasma interaction caused by laser quads overlapping and crossing, the method for determining the characteristic plane where laser quads separate with each other in cylindrical hohlraum has been proposed, and the propagation and overlapping characteristics of the quads from the aspects of polarization characteristics and fractional hot spots have been further analyzed. The results show that during the propagation of multiple quads in cylindrical hohlraum, the inner cone and outer cone separate initially, followed by the separation of adjacent laser quads of both the inner cone and outer cone. When all quads for a single laser entrance hole propagating inside cylindrical hohlraum, the irradiation uniformity of the superposition spots first degrades and improves, then degrades again while propagating from the laser entrance hole to the wall, but peak intensity of hot spots degrades with the increasing of the defocusing distance，and the proportion of hot spots first increases and degrades. In addition, the polarization degree of the multiple laser quads remains almost unchanged during the propagation in hohlraum.