The estimation of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is critical to deconvolve a time-resolved neural activity and get insights on the underlying cognitive processes. Existing methods propose to estimate the HRF using the experimental paradigm (EP) in task fMRI as a surrogate of neural activity. These approaches induce a bias as they do not account for laten-cies in the cognitive responses compared to EP and cannot be applied to resting-state data as no EP is available. In this work, we formulate the joint estimation of the HRF and neu-ral activation signal as a semi blind deconvolution problem. Its solution can be approximated using an efficient alternate minimization algorithm. The proposed approach is applied to task fMRI data for validation purpose and compared to a state-of-the-art HRF estimation technique. Numerical experiments suggest that our approach is competitive with others while not requiring EP information.