Pulse-tube refrigerators are suitable for cooling systems of onboard high-temperature superconducting (HTS) magnets. This is because pulse-tube refrigerators have no moving parts in the cryogenic area and their maintenance cycle is longer than that of other cryocoolers. A novel pulse-tube cooling system that consists of a single compressor and multiple pulse-tubes has been investigated. This system allows uniform cooling of large HTS magnets and minimizes maintenance costs for the compressor. In addition, the refrigeration cycle timing of each pulse-tube can be controlled individually. We examined the same-phase and reverse-phase operations. The COP of the reverse-phase operation was 50 % higher than that of same-phase operation. Numerical simulations indicated a similar result. In the case of the reverse-phase operation, the compressor load was flat, and total energy consumption was reduced. These results show that higher performance was achieved for the reverse-phase operation.