Real-world Electronic Health Records (EHRs) are often plagued by a high rate of missing data. In our EHRs, for example, the missing rates can be as high as 90% for some features, with an average missing rate of around 70% across all features. We propose a Time-Aware Dual-Cross-Visit missing value imputation method, named TA-DualCV, which spontaneously leverages multivariate dependencies across features and longitudinal dependencies both within- and cross-visit to maximize the information extracted from limited observable records in EHRs. Specifically, TA-DualCV captures the latent structure of missing patterns across measurements of different features and it also considers the time continuity and capture the latent temporal missing patterns based on both time-steps and irregular time-intervals. TA-DualCV is evaluated using three large real-world EHRs on two types of tasks: an unsupervised imputation task by varying mask rates up to 90% and a supervised 24-hour early prediction of septic shock using Long Short-Term Memory (LSTM). Our results show that TA-DualCV performs significantly better than all of the existing state-of-the-art imputation baselines, such as DETROIT and TAME, on both types of tasks.