Aims and objectives: This review aims to summarise and evaluate multicomponent interventions focused on improving the competence of family members of people with dementia (PwD) who undertake the caregiving tasks. Background: Caregiver competence is essential for family members of PwD acting as caregivers. Competence affects the physical and mental health of both PwD and caregivers. Many kinds of multicomponent interventions are used to improve caregiver competence. Design: A systematic review. Methods: A literature search from six databases was conducted. Articles published until January 2017 were screened. Intervention studies that measured caregiver competence of family members of PwD as an outcome were included. The Oxford Center Evidence‐based Medicine criteria and the Cochrane Handbook for Systematic Reviews of Interventions were used for quality assessment. Results: Fifteen studies were included, and number of participants was 1096. The characteristics of the included studies and key findings were analysed. Multicomponent interventions may improve the family caregivers’ competence. Caregivers in the intervention group were confident and skilful in managing their role. Conclusion: The intervention design, treatment content and length and intensity of the intervention varied in the included studies. Given that heterogeneity was high, combining these results via narrative synthesis is more appropriate than a meta‐analysis. The current study provides recommendations regarding the formulation and implementation of interventions based on relevant literature. In view of existing research, researchers should conduct an in‐depth study in this area and provide evidence‐based interventions to support family members caring for PwD. Relevance to clinical practice: The competence of family caregivers is essential for the life quality of PwD. To promote the health of the family caregiver and PwD, multicomponent interventions may be appropriate for nurses to practice.