Complex natural tasks likely recruit many different functional brain networks, but it is difficult to predict how such tasks will be represented across cortical areas and networks. Previous electrophysiology studies suggest that task variables are represented in a low-dimensional subspace within the activity space of neural populations. Here we develop a method for recovering task-related state spaces from human fMRI data. We apply this method to data acquired in a controlled visual attention task and a video game task. We find that each task induces distinct brain states that can be embedded in a low-dimensional state space that reflects task parameters, and that attention increases state separation in the task-related subspace. Our results demonstrate that the state space framework offers a powerful approach for modeling human brain activity elicited by complex natural tasks.