Functional magnetic resonance imaging(fMRI) is a non-invasive technique to investigate brain function. It is done by inferring the neural activity by acquiring the MR images when the subject is provided with controllable stimulus. Like other MR techniques, fMRI provides high quality images while suffering the burden of slow data acquisition time and thus the sacrifice in the spatial\temporal resolution. In MR imaging, the scan time is roughly proportional to the number of measurements, therefore sampling fewer measurements can reduce the acquisition time. The recent theory of compressive sensing (CS) states that under certain conditions, images with a sparse representation can be recovered from randomly undersampled measurements. In this dissertation, we propose a recursive sparse reconstruction algorithm to causally reconstruct fMRI sequence from a limited number of measurements. The proposed solution modified-CS-residual uses the time correlation between the image sequences in two novel ways: (a) it uses the fact that the sparsity pattern changes slowly over the time and (b) it also uses the fact that the significant nonzero signal\pixel values also changes slowly. We also demonstrate that our solution provides a very fast and accurate reconstruction while using only about 30% measurements per frame. Extensive experiment results also show the adaptability of modified- CS-residual to different types of blood oxygenation level dependence (BOLD) contrast signals. As a result, our proposed modified-CS-residual can causally reconstruct fMRI sequences and significantly reduce the image acquisition time to enable higher spatial and temporal resolution, which is of great practical use in rapid and dynamic fMRI.