Functional MRI measuring BOLD signal is an increasingly important imaging modality in studying brain functions and neurological disorders. It can be acquired in either a resting-state or a task-based paradigm. Compared to resting-state fMRI, task-based fMRI is acquired while the subject is performing a specific task designed to enhance study-related brain activities. Consequently, it generally has more informative task-dependent signals. However, due to the variety of task designs, it is much more difficult than in resting state to aggregate task-based fMRI acquired in different tasks to train a generalizable model. To resolve this complication, we propose a supervised task-aware network TA-GAT that jointly learns a general-purpose encoder and task-specific contextual information. The encoder-generated embedding and the learned contextual information are then combined as input to multiple modules for performing downstream tasks. We believe that the proposed task-aware architecture can plug-and-play in any neural network architecture to incorporate the prior knowledge of fMRI tasks into capturing functional brain patterns.