Abnormal functional brain connectivity could be considered an endophenotype of psychosis in schizophrenia. Identifying candidate endophenotypes may serve as a tool for elucidating its biological and neural mechanisms. The present study investigated the similarities and differences of features of brain network connectivity between patients and their first-degree relatives. Independent component analysis was conducted on imaging data collected from 34 healthy controls, 33 schizophrenia patients, and 30 unaffected first-degree relatives. The correlation between functional connectivity with neurocognitive performance and clinical symptoms were calculated. Abnormalities of between-network connectivity largely overlapped in patients and first-degree relatives, but the extent of such abnormalities was relatively minor in relatives. Negative connectivity between language networks and executive control networks was impaired in schizophrenia patients and their first-degree relatives, and this decreased connectivity was correlated with performance in language processing. Similar impairments were found in high-visual network and executive network coupling, and this decreased connection was correlated with the severity of positive symptoms in patients. The results indicated that abnormal functional connectivity within and between perceptual systems (i.e., high-visual and language) and executive control networks was related to the generic risk of schizophrenia, which makes it a potential endophenotype for schizophrenia.