Power law scaling is a well-defined physical concept in complexity science that has been used to quantified the dynamic signals across temporal scales. In this research, we aim to investigate the power law scaling of resting-state fMRI signal in schizophrenic and healthy brain and to examine the potential structural properties that may correlate to the altered functional complexity. Brain imaging data of 200 schizophrenia patients and 200 age and sex-matched healthy Han Chinese was retrieved from Taiwan Aging and Mental Illness cohort. Power law scaling was extracted by Pwelch function. In schizophrenia, six brain regions with abnormal complexity were correlated to the regional structural network of grey matter volume (hub at right superior frontal gyrus) and white matter volume at right superior cerebellar peduncle and splenium of the corpus callosum. Moreover, the identified power law scaling was correlated with clinical symptom severity. Our findings suggest that a loss of scale-free brain signal dynamics affecting by brain morphometries proposed the reduced complex brain activity as one of the neurobiological mechanisms in schizophrenia. This research supports "the loss of brain complexity hypothesis" and "the dysconnectivity hypothesis of schizophrenia.", laying potential impact in psychiatry.