Variance is of great significance in measuring the degree of deviation, which has gained extensive usage in many fields in practical scenarios.Although the variance of fuzzy variables with respect to the possibility measure and its properties have been studied before, the variance of fuzzy variables on the basis of the credibility measure has not been formally investigated yet due to the intricate process of calculation.It is acknowledged that the credibility measure is self-dual, which is important both theoretically and practically.Thus, this paper studied the variance of fuzzy variables based upon the credibility measure for better applications.The definition of the variance based on the credibility measure was first put forward by Liu and Liu in 2002.Following this idea, the calculation of the accurate value of the variance for some special fuzzy variables, like the symmetric and asymmetric triangular fuzzy numbers and the Gaussian fuzzy number, is presented in this paper, which turns out to be far more complicated.Therefore, in order to better implement variance in real-life projects like risk control and quality management, this paper suggests a rational upper bound of the variance based on an inequality from a new operational law presented in Zhou et al.(2016), together with its calculation formula, which can largely simplify the calculation process within a reasonable range.Meanwhile, some discussions between the variance and its rational upper bound are presented to show the rationality of the latter.Furthermore, two inequalities regarding the rational upper bound of variance and standard deviation of the sum of two fuzzy variables and their individual variances and standard deviations are proved, respectively.Subsequently, some numerical examples are illustrated to show the effectiveness and the feasibility of the proposed inequalities.