Omnidirectional movement of climbing robots can boost the efficiency of wall operation, reduce the requirement of effective space for steering action, and mitigate the occurrence of instability. In this paper, a new structure of an omnidirectional wall-climbing robot is proposed, which is equipped with an independent omnidirectional wheel mechanism and a two-axis output reduction motor, so that the crawling drive is more reliable and stable. Secondly, the robot is subject to mechanical and magnetic performance analyses to determine the parameters of the combined adhesion of magnetic wheels and block magnets. Finally, based on Adams software, the robot dynamics simulation with examples of vertical and 45° upward crawling are carried out. The results demonstrate that the robot can realize omnidirectional crawling on the wall, which verifies the rationality of the structure scheme and operation principles, providing theoretical references for subsequent prototype development.