The data-driven Intelligent Transportation System (ITS) provides great support to travel decisions and system management but inevitably encounters the issue of data missing in monitoring systems. Hence, network-wide traffic state prediction and imputation is critical to recognizing the system level state of a transportation network. Abundant research works have adopted various approaches for traffic prediction and imputation. However, previous methods ignore the reliability analysis of the predicted/imputed traffic information. Thus, this study originally proposes an attentive graph neural process (AGNP) method for network-level short-term traffic speed prediction and imputation, simultaneously considering reliability. Firstly, the Gaussian process (GP) is used to model the observed traffic speed state. Such a stochastic process is further learned by the proposed AGNP method, which is utilized for inferring the congestion state on the remaining unobserved road segments. Data from a transportation network in Anhui Province, China, is used to conduct three experiments with increasing missing data ratio for model testing. Based on comparisons against other machine learning models, the results show that the proposed AGNP model can impute traffic networks and predict traffic speed with high-level performance. With the probabilistic confidence provided by the AGNP, reliability analysis is conducted both numerically and visually to show that the predicted distributions are beneficial to guide traffic control strategies and travel plans.