The main challenge in bone ultrasound imaging is the large acoustic impedance contrast and sound velocity differ-ences between the bone and surrounding soft tissue. It is difficult for conventional pulse-echo modalities to give accurate ultrasound images for irregular bone boundaries and microstructures using uniform sound velocity assumption rather than getting a prior knowledge of sound speed. To overcome these limitations, this paper proposed a frequency-domain full-waveform inversion (FDFWI) algorithm for bone quantitative imaging utilizing ultrasonic computed tomography (USCT). The forward model was calculated in the frequency domain by solving the full-wave equation. The inverse problem was solved iteratively from low to high discrete frequency components via minimizing a cost function between the modeled and measured data. A quasi-Newton method called the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) was utilized in the optimization process. Then, bone images were obtained based on the estimation of the veloc-ity and density. The performance of the proposed method was verified by numerical examples, from tubular bone phantom to single distal fibula model, and finally with a distal tibia-fibula pair model. Compared with the high-resolution periph-eral quantitative computed tomography (HR-pQCT), the proposed FDFWI can also clearly and accurately presented the wavelength scaled pores and trabeculae in bone images. The results proved that the FDFWI is capable of reconstructing high-resolution ultrasound bone images with sub-millimeter resolution. The parametric bone images may have the potential for the diagnosis of bone disease.