A coaxial spiral tube heat exchanger used for the phase change cold storage of liquid hydrogen cold-chain logistics vehicles is proposed. A three-dimensional heat and flow coupling numerical model of the heat exchanger was established. The influences of parameters such as the hydrogen mass flow rate and mass flow rate of the heat transfer fluid on the outlet temperature of the heat transfer fluid and the phase change cold-storage solidification fraction in the heat exchanger were determined. The results reveal that the outlet temperature of the heat transfer fluid and the cold-storage solidification fraction were closely related to the hydrogen and heat transfer fluid mass flow rates. With the continuous transient heat transfer process between hydrogen and the heat transfer fluid, the outlet temperature of the heat transfer fluid and the cold storage solidification fraction varied rapidly and gradually stabilized. Under the conditions of hydrogen inlet temperature of 30 K, hydrogen mass flow rate of 3.5-6.8 kg/h, hydrogen inlet pressure of 0.6-1.4 MPa, mass flow rate of heat transfer fluid of 414.0-828.0 kg/h, and inlet temperature of heat transfer fluid of 246.0-252.0 K, the shell passage of the spiral tube heat exchanger was not obstructed by solidification of the heat transfer fluid.