The availability of large amounts of data from continuous glucose monitoring (CGM), together with the latest advances in deep learning techniques, have opened the door to a new paradigm of algorithm design for personalized blood glucose (BG) prediction in type 1 diabetes (T1D) with superior performance. However, there are several challenges that prevent the widespread implementation of deep learning algorithms in actual clinical settings, including unclear prediction confidence and limited training data for new T1D subjects. To this end, we propose a novel deep learning framework, Fast-adaptive and Confident Neural Network (FCNN), to meet these clinical challenges. In particular, an attention-based recurrent neural network is used to learn representations from CGM input and forward a weighted sum of hidden states to an evidential output layer, aiming to compute personalized BG predictions with theoretically supported model confidence. The model-agnostic meta-learning is employed to enable fast adaptation for a new T1D subject with limited training data. The proposed framework has been validated on three clinical datasets. In particular, for a dataset including 12 subjects with T1D, FCNN achieved a root mean square error of 18.64±2.60 mg/dL and 31.07±3.62 mg/dL for 30 and 60-minute prediction horizons, respectively, which outperformed all the considered baseline methods with significant improvements. These results indicate that FCNN is a viable and effective approach for predicting BG levels in T1D. The well-trained models can be implemented in smartphone apps to improve glycemic control by enabling proactive actions through real-time glucose alerts.