To meet the working performance demand of cotton pickers, a hydrostatic power shift composite drive system design is proposed. This study aims to enhance the driving function of the cotton picker in various working conditions and improve its adaptability by combining a hydrostatic speed control system with a mechanical power shift structure. To achieve this, a single variable pump + double variable motor closed circuit is adopted. By adjusting the pump and motor displacement in stages, the driving speed of the cotton picker can be optimized for different working conditions. Additionally, the power shift mechanism is employed to increase the speed range and improve the transmission efficiency, enabling higher speeds to be achieved. Firstly, the main components of the composite drive system were calculated and selected, and then AMESim software was used for modeling and simulation analysis, and the results are as follows: When the cotton picker starts and picking operation stage variable displacement pump + fixed displacement dual motor speed control, the highest driving speed is 8.5 km/h. During the field and road transport operation stage fixed displacement pump + variable displacement dual motor speed regulation, the highest speed of 14.5 km/h was achieved in the field. When transferring to the road, the instant mechanical power shift speed and, the highest speed on the road was up to 27.5 km/h. Finally, the field experiment and speed ratio analysis of the drive system was conducted, and the average error of the experimental speed measurement was 0.588%. The speed ratio matching was in line with the design expectation. The results show that the hydrostatic power shift composite drive system designed in this study has good driving adaptability and can effectively meet the functions of cotton picker field picking, transport operation and road transportation in transit, which provides theoretical support for the design of cotton picker chassis drive system.