The coronavirus disease 2019 (COVID-19) pandemic is related to psychological distress. Such distress depends on various factors. We previously reported that hemodialysis patients have more psychological distress than peritoneal dialysis patients among patients on dialysis in the COVID-19 pandemic era. However, no study has reported how psychological distress related to the COVID-19 pandemic depends on renal function in the entire group of chronic kidney disease (CKD) patients. Therefore, the objective of this study was to investigate psychological distress and concerns related to COVID-19 according to CKD stage. This was a cross-sectional study that included 397 CKD patients who visited a hospital from August 2020 to November 2020. Patients responded to questionnaires covering depression (9-item Patient Health Questionnaire, PHQ-9), anxiety (7-item Generalized Anxiety Disorder, GAD-7), psychological impact of event (22-item Impact of Event Scale-Revised, IES-R), insomnia (7-item Insomnia severity Index, ISI), concerns, and precautionary measures about COVID-19. According to eGFR and dialysis status, patients were divided into three groups: (1) patients with CKD stage 12, (2) patients with CKD stage 35 without dialysis, and (3) dialysis patients. The higher the CKD stage, the higher the GAD-7 ( = 0.009) and the ISI score ( = 0.001). When patients with CKD stage 12 and CKD stage 35 (with or without dialysis) were compared, PHQ-9 ( = 0.026), GAD-7 ( = 0.010), and ISI score ( = 0.002) were higher in the CKD stage 3~5 group. However, when comparing those with and without dialysis, only the ISI score ( = 0.008) showed a significant difference. More severe kidney dysfunction in CKD patients was associated with more psychological distress during the COVID-19 pandemic. Therefore, as CKD stage increases, more attention should be paid to the mental care of these patients.