In this paper, a greenhouse tomato picking robot chassis that meets the path cruising and setpoint positioning requirements of robots engaged in greenhouse tomato picking operations in China is designed. Based on the trellis-cultivation growing environment of tomatoes, the basic parameters of the chassis and operating space are analyzed to determine the chassis requirements during picking operations. According to these requirements, a kinematic model of a robot chassis with front-wheel steering and rear-wheel driving is constructed, and the planar positioning principle of the chassis is introduced. SOLIDWORKS is used to simulate and design three-dimensional models of the chassis parts, and the ANSYS WORKBENCH plug-in is used to simulate and analyze the bearing performance of key chassis components. ADAMS is used to simulate and evaluate the motion trajectory of the chassis, and the reasonableness of parameters such as the chassis size, selected materials, and load-bearing performance are verified. Based on the simulation results, a physical system is constructed to experimentally verify the straight-line motion and steering performance of the chassis. The experimental results show that the chassis has good cruising and positioning accuracy and meets the specific requirements of path cruising and setpoint positioning in greenhouse tomato picking operations.