This study proposes an accurate method to estimate human body orientation using a millimeter-wave radar system. Body displacement is measured from the phase of the radar echo, which is analyzed to obtain features associated with the fundamental and higher-order harmonic components of the quasi-periodic respiratory motion. These features are used in body-orientation estimation invoking a novel hierarchical regression model in which a logistic regression model is adopted in the first step to determine whether the target person is facing forwards or backwards; a pair of ridge regression models are employed in the second step to estimate body-orientation angle. To evaluate the performance of the proposed method, respiratory motions of five participants were recorded using three millimeter-wave radar systems; cross-validation was also performed. The average error in estimating body orientation angle was 38.3$^\circ$ and 23.1$^\circ$ using respectively a conventional method with only the fundamental frequency component and our proposed method, indicating an improvement in accuracy by factor 1.7 when using the proposed method. In addition, the coefficient of correlation between the actual and estimated body-orientation angles using the conventional and proposed methods are 0.74 and 0.91, respectively. These results show that by combining the characteristic features of the fundamental and higher-order harmonics from the respiratory motion, the proposed method offers better accuracy.