A superconducting undulator (SCU) prototype with a period of 16 mm and a magnetic gap of 8 mm has been under design and fabrication at the Shanghai Institute of Applied Physics in China since late 2013. The SCU prototype is aimed at obtaining the magnetic field of 0.88 T at the beam axis. A set of support systems was designed to support the cold masses, including superconducting coils, a beam chamber, and thermal shields. A set of self-centering cold mass supports are adopted for the superconducting magnet for the purpose of self-alignment at low temperature. The beam chamber is supported by G-10 spacers against the magnet. The nonmetallic tension rods and spacers are used to support the 60- and 20-K thermal shields, respectively. The heat loads conducted to the cold masses through the supports need to be minimized. This paper presents the design details of the support system.