In the plant factories using stereoscopic cultivation systems, the cultivation plate transport equipment is an essential component of production. However, there are problems, such as high labor intensity, low levels of automation, and poor versatility of existing solutions, that can affect the efficiency of cultivation plate transport processes. To address these issues, this study designed a cultivation plate transport system that can automatically input and output cultivation plates, and can flexibly adjust its structure to accommodate different cultivation frame heights. We elucidated the working principles of the transport system and carried out structural design and parameter calculation for the lift cart, input actuator, and output actuator. In the input process, we used dynamic simulation technology to obtain an optimum propulsion speed of 0.3 m·s−1. In the output process, we used finite element numerical simulation technology to verify that the deformation of the cultivation plate and the maximum stress suffered by it could meet the operational requirements. Finally, operation and performance experiments showed that, under the condition of satisfying the allowable amount of positioning error in the horizontal and vertical directions, the horizontal operation speed was 0.2 m·s−1, the maximum positioning error was 2.87 mm, the vertical operation speed was 0.3 m·s−1, and the maximum positioning error was 1.34 mm. Accordingly, the success rate of the transport system was 92.5–96.0%, and the operational efficiency was 176–317 plates/h. These results proved that the transport system could meet the operational requirements and provide feasible solutions for the automation of plant factory transport equipment.