To effectively deal with structural optimization problems with epistemic uncertainty，an evidence-theory-based reliability design optimization method using approximate moving vectors is proposed. It first converts the evidence variables into probability variables and constructs an equivalent probabilistic reliability-based design optimization model. Through solving this model using the sequential optimization and reliability assessment method，an approximate design point is obtained. Then，the evidence-theory-based reliability analysis is carried out for each constraint at the design point，based on which the approximate shifting vector and deterministic optimization model are established. A new design point is obtained by solving the deterministic optimization problem. Finally，the sequential iteration process composed of equivalent probabilistic reliability-based design optimization and evidence-theory-based reliability analysis is repeated until convergence，and the optimal design point is obtained. The proposed method can convert the nested evidence-theory-based design optimization problem into an iterative solution process，which can effectively reduce its computational cost. The effectiveness of the proposed method is verified by three examples.