Abstract: Traditional structural topology optimization analysis and design is a deterministic physical model based on specific parameters． However，in the actual design process，there are a wide range of uncertainties，which extreme-ly affect the physical properties of the structure． In this study，the variation of structural parameters was quantified by the non-probabilistic reliability based on multi-ellipsoidal convex model，and the topology optimization problem with uncertain but bounded parameter continuum structure was studied． Firstly，the reliability topology optimization model with variable uncertainty was established，taking the structural design quality minimization as the objective function． Then，based on the geometric meaning of the reliability index，the non-probability model was used to find the design point that satisfies the target reliability index constraint． On this basis，the interval Chebyshev zero poly-nomial was applied to approximate the real limit state function of the normalized random variable，and the single-loop reliability algorithm was used to calculate the optimal design points value under the corresponding target relia-bility index，so that the optimization problem of non-probability reliability can be transformed into deterministic op-timization problem． The effectiveness of the method was illustrated by two numerical examples． The results show that，compared with the deterministic structural topology optimization design，the reliability topology optimization with random variables can obtain more reliable topology structure．

Key words: structural topology optimization, uncertainty, non-probabilistic reliability, Chebyshev polynomial, convex model