Spatial source phase (SSP), derived from complex-valued functional magnetic resonance imaging (fMRI) data by datadriven methods, has unique capacity of identifying blood oxygenation-level dependent (BOLD)-related voxels from noisy voxels regardless of their amplitudes. However, the use of SSP constraint in sparse representation algorithms have rarely been studied. This study proposes a sparse representation method using SSP hard thresholding to achieve the sparsity of spatial components, enabling the use of initially complex-valued fMRI data and retaining the brain information embedded in noisy voxels and weak BOLDrelated voxels with small phase values. Rank-1 matrix estimation is applied to sequentially update dictionary atoms and corresponding spatial components, followed by hard thresholding on spatial components based on SSP. The proposed method is evaluated using both simulated and experimental complex-valued data. The results show that the proposed method yields better performance than a complexvalued dictionary learning algorithm when using initially acquired complex-valued task-related fMRI data.