Brain-wide association study (BWAS) is analogous to the successful genome-wide association study (GWAS) in the genetics field. It aims to identify the voxel-wise functional connectome variations associated with complex traits. Although it has been applied to several mental disorders, such as schizophrenia, autism and depression, its statistical foundations are still lacking. Therefore, we herein report the development of a rigorous statistical framework for link-wise significance testing and theoretical power analysis based on the random field theory. Peak- and cluster-level inferences are generalized to analyze functional connectivities. A novel method to identify phenotype associated voxels based on functional connectivity pattern is also proposed. Our method reduces the computational complexity of permutation-based approach in controlling the false positive rate and provides robust and reproducible findings in several real datasets, such as the 1000 Functional Connectomes Project (1000 FCP), Autism Brain Imaging Data Exchange (ABIDE), Center for Biomedical Research Excellence (COBRE) and others.