In indirect-drive inertial confinement fusion facilities, aimed at the spherical hohlraum structure and the laser quads configuration, and based on the beam smoothing scheme implemented by the combined use of smoothing by spectral dispersion, continuous phase plate (CPP) and polarization control plate, the propagation model of laser quads in the spherical hohlraum has been built up. Because of the high spherical symmetry of spherical hohlraum and laser quads configuration, the plane of the laser entrance hole (LEH) is taken as the observation plane for analyzing the characteristics of laser quads propagating through the LEH, and the LEH closure problem is mainly analyzed. A series of concentric spherical surfaces have been taken as the observation surfaces for analyzing the propagation characteristics of laser quads in spherical hohlraum and the illumination characteristics on hohlraum wall. Simulation results indicate that, When different incident angles of the laser quads are used with the same CPP, with the increasing of the laser quads incident angle, the laser energy injection rate at LEH decreases and it is easier to bring about the LEH closure, while the cross and overlap of laser quads reduce gradually, the illumination uniformity on the hohlraum wall slightly improves and the duty ratio of all laser quads on the hohlraum wall is also improved, which is helpful for achieving the irradiation uniformity of the target. As different incident angles of the laser quads using the different CPP, the LEH closure problem is improved, While the duty ratio of the hohlraum wall decreased. In practical applications, it is required to design the laser quads incident angle appropriately by taking the LEH injection rate and the LEH closure problem, the overlap and uniformity of laser quads in hohlraum, as well as the irradiation uniformity of all quads and the duty ratio on hohlraum wall into consideration.