This study presents a hybrid reliability-based topology optimization (RBTO) method for handling epistemic and aleatory uncertainties. First, we establish a new triple-nested RBTO model based on fuzzy and probabilistic theory for describing the multi-source uncertainties. Subsequently, an efficient single-loop optimization method is proposed to degrade the triple-nested optimization problem into a deterministic optimization problem using the Karush–Kuhn–Tucker optimality condition. Furthermore, the sensitivities of the hybrid reliability constraint with respect to the random probabilistic variables, fuzzy variables, and deterministic design variables are derived using the adjoint variable method. Finally, a cantilever beam example, an L-shape beam design and a 3D example are tested to verify the validity of the proposed single-loop method. •A novel RBTO model with nested triple loops is created under SIMP framework.•An efficient single-loop hybrid RBTO method is established.•The aleatory and epistemic uncertain sensitivity calculation technique is developed.•2D and 3D topology optimization examples illustrate the superiority of the proposed method.