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We propose STSRNet, a joint space-time super-resolution deep learning based model for time-varying vector field data. Our method is designed to reconstruct high temporal resolution (HTR) and high spatial resolution (HSR) vector fields sequence from the corresponding low-resolution key frames. For large scale simulations, only data from a subset of time steps with reduced spatial resolution can be stored for post-hoc analysis. In this paper, we leverage a deep learning model to capture the non-linear complex changes of vector field data with a two-stage architecture: the first stage deforms a pair of low spatial resolution (LSR) key frames forward and backward to generate the intermediate LSR frames, and the second stage performs spatial super-resolution to output the high-resolution sequence. Our method is scalable and can handle different data sets. We demonstrate the effectiveness of our framework with several data sets through quantitative and qualitative evaluations.