Intuitionistic fuzzy number as the generalization of fuzzy number has better capability to model uncertain data in management decision science and mathematical engineering problem. In this paper, we present a new definition of possibilistic mean and variance for generalized trapezoidal intuitionistic fuzzy number (GTIFN), and show that some properties of crisp mean and variance in probability theory are preserved by possibilistic mean and variance of generalized trapezoidal intuitionistic fuzzy numbers. We also discuss some notes on possibilistic variance of GTIFNs and get the important relationships between the proposed two possibilistic variances of generalized trapezoidal intuitionistic fuzzy number.