To improve image quality and CT number accuracy of fast-scan low-dose cone-beam computed tomography (CBCT) through a deep-learning convolutional neural network (CNN) methodology for head-and-neck (HN) radiotherapy. Fifty-five paired CBCT and CT images from HN patients were retrospectively analysed. Among them, 15 patients underwent adaptive replanning during treatment, thus had same-day CT/CBCT pairs. The remaining 40 patients (post-operative) had paired planning CT and 1st fraction CBCT images with minimal anatomic changes. A 2D U-Net architecture with 27-layers in 5 depths was built for the CNN. CNN training was performed using data from 40 post-operative HN patients with 2080 paired CT/CBCT slices. Validation and test datasets include 5 same-day datasets with 260 slice pairs and 10 same-day datasets with 520 slice pairs, respectively. To examine the impact of differences in training dataset selection and network performance as a function of training data size, additional networks were trained using 30, 40 and 50 datasets. Image quality of enhanced CBCT images were quantitatively compared against the CT image using mean absolute error (MAE) of Hounsfield units (HU), signal-to-noise ratio (SNR) and structural similarity (SSIM). Enhanced CBCT images reduced artifact distortion and improved soft tissue contrast. Networks trained with 40 datasets had imaging performance comparable to those trained with 50 datasets and outperformed those trained with 30 datasets. Comparison of CBCT and enhanced CBCT images demonstrated improvement in average MAE from 172.73 to 49.28 HU, SNR from 8.27 to 14.25 dB, and SSIM from 0.42 to 0.85. The image processing time is 2 s per patient using a NVIDIA GeForce GTX 1080 Ti GPU. The proposed deep-leaning methodology was fast and effective for image quality enhancement of fast-scan low-dose CBCT. This method has potential to support fast online-adaptive re-planning for HN cancer patients.