Disturbance of glucose metabolism may be implicated in cognitive deficits of schizophrenia in its early phases. Many studies have reported the important role of widespread disruption of white matter (WM) connectivity in pathogenesis, cognitive deficit and psychopathology of schizophrenia. However, no study has investigated their inter-relationships in drug-naive first episode (DNFE) patients with schizophrenia. Glucose metabolism parameters including fasting glucose, insulin and homeostasis model of assessment-insulin resistance (HOMA-IR) index, cognitive performance on the MATRICS Consensus Cognitive Battery (MCCB) and the voxel-wised WM fractional anisotropy (FA) values were examined using DTI in 39 DNFE schizophrenia and 31 control subjects. The Positive and Negative Syndrome Scale was utilized for clinical symptoms. The patients showed significantly greater fasting plasma levels of glucose and insulin and HOMA-IR, and poorer cognitive scores, together with widespread reduced FA values in five brain areas, including left and right corpus callosum, superior longitudinal fasciculus, posterior thalamic radiation, and corona radiata (all p < 0.05). Association analysis showed that glucose level was positively associated with Digital Sequence Test and Continuous Performance Test, but negatively with FA values in posterior thalamic radiation and left corpus callosum in patients (all p < 0.05). Furthermore, multiple regression analysis revealed that the interactions of glucose × FA in left corpus callosum, longitudinal fasciculus and corona radiata were independent contributors to the Brief Visuospatial Memory Test (BVMT) of MCCB, while the interaction of glucose × FA in left corpus callosum, or in longitudinal fasciculus was associated with MCCB mazes and Trail Making A Test, respectively. Therefore, abnormal glucose metabolism, cognitive impairment and widespread disruption of WM structure occur in an early course of schizophrenia onset. An interaction between glucose metabolism abnormality and the WM dysconnectivity may lead to cognitive impairment.