We have investigated the properties of the ergosphere and the energy extraction by Penrose process in a Konoplya-Zhidenko rotating non-Kerr black hole spacetime. We find that the ergosphere becomes thin and the maximum efficiency of energy extraction decreases as the deformation parameter increases. For the case with , the positive deformation parameter yields that the maximum efficiency is lower than that in the Kerr black hole with the same rotation parameter. However, for the superspinning case with , we find that the maximum efficiency can reach so high that it is almost unlimited as the positive deformation parameter is close to zero, which is a new feature of energy extraction in such kind of rotating non-Kerr black hole spacetime.

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