We have developed a prototype half-wave plate (HWP) based polarization modulator (PMU) for Cosmic Microwave Background polarization measurement experiments. We built a 1/10 scaled PMU that consists of a 50 mm diameter five-layer achromatic HWP with a moth-eye broadband anti-reflection sub-wavelength structure mounted on a superconducting magnetic bearing. The entire system has cooled below 20 K in a cryostat chamber that has two millimeter-wave transparent windows. A coherent source and the diode detector are placed outside of the cryostat and the millimeter-wave goes through the PMU in the cryostat. We have measured the modulated signal by the PMU, analyzed the spectral signatures, and extracted the modulation efficiency over the frequency coverage of 34-161 GHz. We identified the peaks in the optical data, which are synchronous to the rotational frequency. We also identified the peaks that are originated from the resonance frequency of the levitating system. We also recovered the modulation efficiency as a function of the incident electromagnetic frequency and the data agrees to the predicted curves within uncertainties of the input parameters, i.e.The indices of refraction, thickness, and angle alignment. Finally, we discuss the implication of the results when this is applied to the LiteBIRD low-frequency telescope.