The Joule–Thomson (J–T) cryocooler is widely used in a variety of infrared devices. Maximizing the cooling capacity in finite structures is one of the foremost problems in J-T cryocooler miniaturization. In this study, a one-dimensional model based on the thermodynamic properties of real gas and heat leakage of components is established. The effects of three structural parameters (fin height, fin thickness, and fin pitch) used in a helical finned tube heat exchanger on the performance of a cryocooler are calculated and optimized using a genetic algorithm. The results show that the calculated data are in good agreement with the experimental data. In the specific working conditions and structural parameters employed, an increase in fin height and fin thickness would increase the entropy production and cooling capacity of the cold end of the heat exchanger, whereas an increase in fin pitch would have the opposite effect. Optimal parameters exist for maximizing the cooling capacity of the heat exchanger in this study. The analytical method established in this study could provide a simple and effective means of optimizing and designing a J–T in engineering applications.