For people with Type 1 diabetes (T1D), forecasting of \red{blood glucose (BG)} can be used to effectively avoid hyperglycemia, hypoglycemia and associated complications. The latest continuous glucose monitoring (CGM) technology allows people to observe glucose in real-time. However, an accurate glucose forecast remains a challenge. In this work, we introduce GluNet, a framework that leverages on a personalized deep neural network to predict the probabilistic distribution of short-term (30-60 minutes) future CGM measurements for subjects with T1D based on their historical data including glucose measurements, meal information, insulin doses, and other factors. It adopts the latest deep learning techniques consisting of four components: data pre-processing, label transform/recover, multi-layers of dilated convolution neural network (CNN), and post-processing. The method is evaluated in-silico for both adult and adolescent subjects. The results show significant improvements over existing methods in the literature through a comprehensive comparison in terms of root mean square error (RMSE) (8.88 ± 0.77 mg/dL) with short time lag (0.83 ± 0.40 minutes) for prediction horizons (PH) = 30 mins (minutes), and RMSE (19.90 ± 3.17 mg/dL) with time lag (16.43 ± 4.07 mins) for PH = 60 mins for virtual adult subjects. In addition, GluNet is also tested on two clinical data sets. Results show that it achieves an RMSE (19.28 ± 2.76 mg/dL) with time lag (8.03 ± 4.07 mins) for PH = 30 mins and an RMSE (31.83 ± 3.49 mg/dL) with time lag (17.78 ± 8.00 mins) for PH = 60 mins. These are the best reported results for glucose forecasting when compared with other methods including the neural network for predicting glucose (NNPG), the support vector regression (SVR), the latent variable with exogenous input (LVX), and the auto regression with exogenous input (ARX) algorithm.