A Stirling-type pulse tube cryocooler (PTC) with a superconducting linear motor for the compressor unit was developed and tested. The compressor was able to produce oscillating mass flow and pulsating pressure at low temperature environment near 80 K and transmitted compression work efficiently to the cold-end of the pulse tube cryocooler. Although he efficiency of the linear compressor excited by copper coil usually high, the superconducting linear compressor can further improve the system efficiency by eliminating the Joule heating loss of copper coil. The first attempt of superconducting linear compressor did not attain the expected high efficiency. We suspected the AC losses in the superconducting linear motor as one of the main factors to degrade the performance of the linear compressor. This paper describes the detailed investigation of AC losses in the superconducting linear compressor, primarily carried out by experiment. To extract the AC loss of the copper bobbin in the high temperature superconductor (HTS) coil assembly, we replaced the copper structure by glass fiber reinforced polymer (GFRP) bobbins and manufactured the same HTS coil. AC losses of both HTS coils were measured and compared each other. The results revealed out that the copper bobbins in the HTS coil generated 8.7 W of the additional AC loss with current of 7 A(rms) and operating frequency of 50 Hz. The copper structure should be replaced to improve the performance of superconducting linear compressor, and an alternative cooling method is required.