Data generated from the Internet of Things (IoT) devices in smart spaces are utilized in a variety of fields such as context recognition, service recommendation, and anomaly detection. However, the missing values in the data streams of the IoT devices remain a challenging problem owing to various missing patterns and heterogeneous data types from many different data streams. In this regard, while we were analyzing the dataset collected from a smart space with multiple IoT devices, we found a continuous missing pattern that is quite different from the existing missing-value patterns. The pattern has blocks of consecutive missing values over a few seconds and up to a few hours. Therefore, the pattern is a vital factor to the availability and reliability of IoT applications; yet, it cannot be solved by the existing missing-value imputation methods. Therefore, a novel approach for missing-value imputation of the continuous missing pattern is required. We deliberate that even if the missing values of the continuous missing pattern occur in one data stream, missing-values imputation is possible through learning other data streams correlated with this data stream. To solve the missing values of the continuous missing pattern problem, we analyzed multiple IoT data streams in a smart space and figured out the correlations between them that are the interdependencies among the data streams of the IoT devices in a smart space. To impute missing values of the continuous missing pattern, we propose a deep learning-based missing-value imputation model exploiting correlation information, namely, the deep imputation network (DeepIN), in a smart space. The DeepIN uses that multiple long short-term memories are constructed according to the correlation information of each IoT data stream. We evaluated the DeepIN on a real dataset from our campus IoT testbed, and the experimental results show that our proposed approach improves the imputation performance by 57.36% over the state-of-the-art missing-value imputation algorithm. Thus, our approach can be a promising methodology that enables IoT applications and services with a reasonable missing-value imputation accuracy (80 similar to 85%) on average, even if a long-term block of values is missing in IoT environments.