In application to functional magnetic resonance imaging (fMRI) data analysis, a number of data fusion algorithms have shown success in extracting interpretable brain networks that can distinguish two groups such two populations-patients with mental disorder and the healthy controls. However, there are situations where more than two groups exist such as the fusion of multi-task fMRI data. Therefore, in this work we propose the use of IVA to effectively extract information that is able to distinguish across multiple groups when applied to data fusion. The performance of IVA is investigated using a simulated fMRI-like data. The simulation results illustrate that IVA with multivariate Laplacian distribution and second-order statistics (IVA-L-SOS) yields better performance compared to joint independent component analysis and IVA with multivariate Gaussian distribution in terms of both estimation accuracy and robustness. When applied to real multi-task fMRI data, IVA-L-SOS successfully extract task-related brain networks that are able to distinguish three tasks.