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This paper proposed a mini-max fusion strategy in distributed multi-sensor system, which aims to minimize the worst-case squared estimation error when the cross-covariances between local sensors are unknown. The resulted estimation fusion is called as the Chebyshev fusion estimation (CFE) which is actually a non-linear combination of local estimations. We have also proofed that the CFE is better than any local estimator in the sense of minimize the worst-case squared estimation error. Moreover, a sensitive analysis about the choice of the support bound is carried out. The simulations illustrate that the proposed CFE is a robust fusion and more accurate than the previous covariance intersection (CI) estimation fusion method.