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Accurate prediction for kurtosis of bearing vibration signal is helpful to find out the fault of bearing as soon as possible. Kurtosis prediction of bearing vibration signal based on wavelet packet transform and Cauchy kernel relevance vector regression algorithm is presented in this article. Here, kurtosis of bearing vibration signal can be decomposed into several sub-signals with different frequency ranges based on wavelet packet transform; the prediction models of these decomposed signals can be established by the Cauchy kernel relevance vector regression models with their respective appropriate embedding dimensions, and grid method is used to select the appropriate kernel parameter of each Cauchy kernel relevance vector regression model. The experimental results show that it is feasible for the proposed combination scheme to improve the prediction ability of Cauchy kernel relevance vector regression algorithm for kurtosis of bearing vibration signal.