The work aims to design a three-axis transport robot to transport the goods on the shelves to the destination directly, thus realizing the purpose of transporting the goods to the people. The three-dimensional model and finite element model were established with SolidWorks and Workbench software, and the chassis mechanism and the lifting mechanism were designed in detail. The modal analysis of chassis structure was conducted, and the external excitation source was analyzed. The plates on both sides used to install the lifting mechanism were the main factor affecting the dynamic characteristics. The chassis structure designed would not resonate due to the external excitation. The proposed transport robot is featured by novel structure and reasonable design. It can be widely applied in many cases, such as picking goods, storing and transporting artifacts, and it has higher application value.