The purpose of this study was to directly and quantitatively measure BMD from Cone-beam CT (CBCT) images by enhancing the linearity and uniformity of the bone intensities based on a hybrid deep-learning model (QCBCT-NET) of combining the generative adversarial network (Cycle-GAN) and U-Net, and to compare the bone images enhanced by the QCBCT-NET with those by Cycle-GAN and U-Net. We used two phantoms of human skulls encased in acrylic, one for the training and validation datasets, and the other for the test dataset. We proposed the QCBCT-NET consisting of Cycle-GAN with residual blocks and a multi-channel U-Net using paired training data of quantitative CT (QCT) and CBCT images. The BMD images produced by QCBCT-NET significantly outperformed the images produced by the Cycle-GAN or the U-Net in mean absolute difference (MAD), peak signal to noise ratio (PSNR), normalized cross-correlation (NCC), structural similarity (SSIM), and linearity when compared to the original QCT image. The QCBCT-NET improved the contrast of the bone images by reflecting the original BMD distribution of the QCT image locally using the Cycle-GAN, and also spatial uniformity of the bone images by globally suppressing image artifacts and noise using the two-channel U-Net. The QCBCT-NET substantially enhanced the linearity, uniformity, and contrast as well as the anatomical and quantitative accuracy of the bone images, and demonstrated more accuracy than the Cycle-GAN and the U-Net for quantitatively measuring BMD in CBCT.