We present a breadboard model development status of the polarization modulator unit (PMU) for a low-frequency telescope (LFT) of the LiteBIRD space mission. LiteBIRD is a next-generation cosmic microwave background polarization satellite to measure the primordial B-mode with the science goal of σr < 0.001. The baseline design of LiteBIRD consists of reflective low-frequency and refractive medium-and-high-frequency telescopes. Each telescope employs the PMU based on a continuous rotating half-wave plate (HWP) at the aperture. The PMU is a critical instrument for the LiteBIRD to achieve the science goal because it significantly suppresses 1/f noise and mitigates systematic uncertainties. The LiteBIRD LFT PMU consists of a broadband achromatic HWP and a cryogenic rotation mechanism. In this presentation, we discuss requirements, design and systematic studies of the PMU, and we report the development status of the broadband HWP and the space-compatible cryogenic rotation mechanism.