Purpose To estimate dynamic off-resonance due to vigorous body motion in accelerated fMRI of awake behaving non-human primates (NHPs) using the standard EPI 3-line navigator, in order to attenuate the effects of time-varying off-resonance on the reconstruction. Methods In NHP fMRI the animal’s head is usually head-posted, and the dynamic off-resonance is mainly caused by motion in body parts that are distant from the brain and have low spatial frequency. Hence, off-resonance at each frame can be approximated as a spatially linear perturbation of the off-resonance at a reference frame, and is manifested as a relative linear shift in k-space. Using GRAPPA operators, we estimated these shifts by comparing the 3-line navigator at each time frame with that at the reference frame. Estimated shifts were then used to correct the data at each frame. The proposed method was evaluated in phantom scans, simulations, and in vivo data. Results The proposed method is shown to successfully estimate low-spatial order dynamic off-resonance perturbations, including induced linear off-resonance perturbations in phantoms, and is able to correct retrospectively corrupted data in simulations. Finally, it is shown to reduce ghosting artifacts and geometric distortions by up to 20% in simultaneous multi-slice in vivo acquisitions in awake-behaving NHPs. Conclusion A method is proposed that does not need any sequence modification or extra acquisitions and makes accelerated awake behaving NHP imaging more robust and reliable, reducing the gap between what is possible with NHP protocols and state-of-the-art human imaging.