A special purpose gamma-ray computed tomography scanner has been developed for precise measurements of bone density in the human appendicular skeleton. Details of the scanner's hardware and of the software organization for system control and data analysis are given, together with an outline of the theoretical basis for conversion of measured linear attenuation coefficients to physical bone densities. Performance of the system was evaluated on bone-like phantoms. Clinically, a precision of +/- 0.5% is obtained for bone density determinations. This device is being used in experimental studies and clinical investigations.