Multi-modal data analysis techniques, such as the Parallel Independent Component Analysis (pICA), are essential in neuroscience, medical imaging and genetic studies. The pICA algorithm allows the simultaneous decomposition of up to two data modalities achieving better performance than separate ICA decompositions and enabling the discovery of links between modalities. However, advances in data acquisition techniques facilitate the collection of more than two data modalities from each subject. Examples of commonly measured modalities include genetic information, structural magnetic resonance imaging (MRI) and functional MRI. In order to take full advantage of the available data, this work extends the pICA approach to incorporate three modalities in one comprehensive analysis. Simulations demonstrate the three-way pICA performance in identifying pairwise links between modalities and estimating independent components which more closely resemble the true sources than components found by pICA or separate ICA analyses. In addition, the three-way pICA algorithm is applied to real experimental data obtained from a study that investigate genetic effects on alcohol dependence. Considered data modalities include functional MRI (contrast images during alcohol exposure paradigm), gray matter concentration images from structural MRI and genetic single nucleotide polymorphism (SNP). The three-way pICA approach identified links between a SNP component (pointing to brain function and mental disorder associated genes, including BDNF, GRIN2B and NRG1), a functional component related to increased activation in the precuneus area, and a gray matter component comprising part of the default mode network and the caudate. Although such findings need further verification, the simulation and in-vivo results validate the three-way pICA algorithm presented here as a useful tool in biomedical data fusion applications. © 2014 Elsevier Inc.