This paper handles the new information entropy measure and divergence measure associated with intuitionistic fuzzy variables (IFVs). Based on credibility distribution and credibility measure of intuitionistic fuzzy variable, the credibility entropy formulas of discrete and continuous IFVs are proposed and some of their properties are investigated. The cross-entropy of intuitionistic fuzzy variable and its relationship with credibility entropy are then discussed. Finally, some numerical examples are given to illustrate the practicability of the presented credibility entropy and cross-entropy of intuitionistic fuzzy variable. Also, we make some comparative analysis on the credibility cross-entropy measure and some existing distance measures of IFVs in the pattern recognition problem.