A system capable of rapidly cooling magnets from room temperature to below 60 K was designed, in order to reduce the resource consumption and economic cost of cooling the low temperature superconducting magnet of magnetic resonance imaging (MRI). Furthermore, the design optimization and in-depth analysis were carried out by numerical simulation based on its mathematical physics model. A self-developed single-stage Stirling cryocooler with large cooling capacity was used as the cold source of this system, comprising a cryogenic fan, control valves and one helium gas cylinder. Results showed that the cooling performance can be improved by optimizing the operating parameters of system, of which the pressure and flow rate of helium gas were particularly critical, because they can significantly affect the pressure drop and heat transfer and further affect the cooling time and temperature that the magnet could ultimately attain. Moreover, the current cold end heat exchanger performance of Stirling cryocooler still had space for promotion. This system can achieve a fast cooling rate at helium pressure of 0.3 MPa and flow rate of 13 m/s through parameter optimization. A superconducting magnet weighing 2 tons can be cooled to below 60 K from room temperature within 73.5 h based on the above condition, which showed that it had the potential to achieve low energy consumption and high efficiency of cooling MRI low temperature superconducting magnet in practical applications.