The fuzzy and random variables usually exist in the uncertainty structural simultaneously. And for some structures, the failure criterion is also not deterministic and is a gradual failure process, which usually be described by the fuzzy theory. In order to analyse the hybrid uncertain propagation for the structure system with the fuzzy failure criterion, a new analysis model is established based on non-probabilistic theory in this paper. The fuzzy failure criterion is handled with an auxiliary fuzzy variable of the response. Through introducing the random variable obeying [0, 1] uniform distribution into the membership level of fuzz variables, the input fuzzy variables can be regarded as the interval variables at the random set levels. When the random input variables take their nominal values, the original reliability problem only contains the interval variables. Based on non-probabilistic theory, the second level performance function is constructed, which is the function of the random levels and random input variables. The Kriging model is employed to construct the surrogate of the second level function for reducing the computational cost. A classical engineering example is used to demonstrate the feasibility and rationality of the proposed model and the efficient and precision of the proposed algorithm.