A number of reconstruction methods have been proposed recently for accelerated functional Magnetic Resonance Imaging (fMRI) data collection. However, existing methods suffer with the challenge of greater artifacts at high acceleration factors. This paper addresses the issue of accelerating fMRI collection via undersampled k-space measurements combined with the proposed Double Temporal Sparsity based Reconstruction (DTSR) method with the l1 -l1 norm constraint. The robustness of the proposed DTSR method has been thoroughly evaluated both at the subject level and at the group level on real fMRI data. Results are presented at various acceleration factors. Quantitative analysis in terms of Peak Signal-to-Noise Ratio (PSNR) and other metrics, and qualitative analysis in terms of reproducibility of brain Resting State Networks (RSNs) demonstrate that the proposed method is accurate and robust. In addition, the proposed DTSR method preserves brain networks that are important for studying fMRI data. Compared to the existing accelerated fMRI reconstruction methods, the DTSR method shows promising potential with an improvement of 10-12dB in PSNR with acceleration factors upto 3.5. Simulation results on real data demonstrate that DTSR method can be used to acquire accelerated fMRI with accurate detection of RSNs.