Recent research suggested that the error entropy (EE) criteria could be used to achieve a better error distribution in estimation, adaptation and learning. In this paper, we formulated the adaptive inverse control under a generalized error entropy criterion, i.e. (h, ø)-entropy criterion, and derived the associated error-entropy minimization algorithm. Several detailed schemes of adaptive filtering and inverse control under (h, ø)-entropy criterion were also presented. Finally, a simple simulation example has illustrated the effectiveness and advantages of this new method.