We propose a novel omnidirectional step-climbing robot capable of moving in all directions on the ground and climbing steps. To achieve this, we present the construction and design of a robot equipped with four innovative equilateral triangle-type chain wheels (ETCWs) and two elevation-adjusting modules (EAMs). The designed ETCWs, which are arranged around multiple roller assemblies, facilitate step-climbing by creating small gaps between roller assemblies when the wheel comes in contact with the uneven ground. The corners of steps become stuck in the small gaps of ETCWs, preventing slipping during step-climbing. The designed EAM is used to adjust the height of the robot’s base frame adaptively to avoid terrain obstacles, referring to signals from front ultrasonic sensors. Static analysis models for the main support frames are developed, and a case study on motion trajectory planning is also conducted.