S. Karkaus, K. Demirci, and O. Duman in 2008 studied the statistical convergence of a single sequence over Intuitionistic fuzzy normed space(\textbf{IFNS}). M. Mursaleen in 2009, generalized the above work for double sequences over IFNS. The present article is the study of statistical convergence of triple sequence and triple Cauchy sequences on IFNS. In addition, the article includes examples in support of some definitions and theorems. Furthermore, we examined the proof of the completeness of special sequence space.