Inference with incomplete data, especially non-ignorable, is one of the challenging tasks in data analysis. Moreover, it is well known that results obtained from incomplete data are prone to bias. Parameter estimation with non-ignorable missing data is even more challenging to handle and extract useful information. This paper proposes a method based on the Influential tilting resampling approach (ITRA) to handle non-ignorable missing data for inference on the mean. One of the bases of the proposed approach is assuming that the model for the non-respondents corresponds to an exponential tilting of the respondents’ model, and the specified function in the tilted model is the influential function of the functional (parameter) of interest. Extensive simulation studies were conducted to investigate the performance of the proposed methods. We provided the theoretical justification, as well as application to real data.