Deep Learning (DL) has achieved great success in many real applications. Despite its success, there are some main problems when deploying advanced DL models in database systems, such as hyper-parameters tuning, the risk of overfitting, and lack of prediction uncertainty. In this paper, we study cardinality estimation for SQL queries with a focus on uncertainty, which we believe is important in database systems when dealing with a large number of user queries on various applications. With uncertainty ensured, instead of trusting an estimator learned as it is, a query optimizer can explore other options when the estimator learned has a large variance, and it also becomes possible to update the estimator to improve its prediction in areas with high uncertainty. The approach we explore is different from the direction of deploying sophisticated DL models in database systems to build cardinality estimators. We employ Bayesian deep learning (BDL), which serves as a bridge between Bayesian inference and deep learning.The prediction distribution by BDL provides principled uncertainty calibration for the prediction. In addition, when the network width of a BDL model goes to infinity, the model performs equivalent to Gaussian Process (GP). This special class of BDL, known as Neural Network Gaussian Process (NNGP), inherits the advantages of Bayesian approach while keeping universal approximation of neural network, and can utilize a much larger model space to model distribution-free data as a nonparametric model. We show that our uncertainty-aware NNGP estimator achieves high accuracy, can be built very fast, and is robust to query workload shift, in our extensive performance studies by comparing with the existing approaches.