Time series data related to traffic and air quality are useful indicators for urban planning but they frequently have missing values. Imputation of multi-sensor time series data is thus a vital pre-processing step for forecasting, anomaly detection and other downstream tasks. We develop an efficient architecture – Sparse Attention-based Imputation Network for Time series (SAINT) – which outperforms the state-of-the-art imputation networks. Efficiency is achieved by separating the computations on the space-time product graph sequentially into channel independent temporal attention and sparse space-time transformer. This channel independent network can reduce overfitting to effectively represent general temporal patterns. Sparse space-time transformer performs message passing on the spatial graph conditioned on time. We consider real-world datasets for evaluation – PEMS-BAY, METR-LA and AQI – which are gathered from sensor networks in major cities. We demonstrate the effectiveness and robustness of SAINT across complex missing data scenarios. Additionally, SAINT generalizes well to short-term forecasting and is practical for long-term forecasting with limited resources.