A relative entropy version of Havrda-Charvat’s \(\alpha\)-entropy [J. Havrda and F. Charvát, Kybernetika 3, 30–35 (1967; Zbl 0178.22401)] is introduced and its characterization by specifying the conditions of degree of entropy increase, symmetry and continuity is given. Properties of relative \(\alpha\)-entropy for a continuous system analogous to those which hold for the usual relative entropy such as positivity, monotonicity, integral representation, lower semicontinuity and joint convexity are discussed.