Many recently developed data-driven fault estimation methods are restricted to minimum-phase systems so that their practical applications are limited. In this paper, the data-driven fault estimation for non minimum phase (NMP) systems is studied, for which the main difficulty is that the unstable zeros of an NMP system will result in a growing fault-estimation error. To deal with this problem, the inverse of an NMP system is equivalently formulated as a mixed causal and anti-causal system, and the proposed fault estimator is the sum of a stable causal filter and a stable anti-causal filter. The proposed fault estimator is shown to be asymptotically unbiased and its performance is demonstrated by numerical simulations. (C) 2018 Elsevier Ltd. All rights reserved.