Sleep disturbances have been reported in obsessive-compulsive disorder (OCD) patients, with heterogeneous results. The aim of our study was to assess sleep function in OCD and to investigate the relationship between sleep and the severity of obsessive-compulsive (OC) symptoms, depressive symptoms and trait anxiety. Sleep quality was measured in 61 OCD patients and 100 healthy controls (HCs) using the Pittsburgh Sleep Quality Index (PSQI). Multiple linear regression was conducted to explore the association between sleep and psychopathological measures; a mediation analysis was also performed. OCD patients showed poor sleep quality and more sleep disturbances compared to HCs. The severity of depression, trait anxiety and OC symptomatology were correlated with poor sleep quality. Multiple linear regression analyses controlling for potential confounders revealed that the severity of depression and trait anxiety were independently related to poor sleep quality in OCD. A mediation analysis showed that both the severity of trait anxiety and depression mediate the relationship between the severity of OC symptoms and poor sleep quality among patients with OCD. Our findings support the existence of sleep disturbances in OCD. Trait anxiety and depression play a key role in sleep quality among OCD patients. The online version contains supplementary material available at 10.1186/s12888-021-03038-z