There are certain forms of integral averages which are known as Dirichlet averages according to their Dirichlet measure. The theory of multiple types of Dirichlet averaging was introduced by Carlson (1969-1987). Again this has been analyzed by others Mathematicians like Khan et al. (2017), Gupta and Aggarwal (1990-91), Saxena et al. (2010), Sharma and Jain (2006-07), Kilbas and Kattuvetty (2008), Deora and Banerjee (1993), A.K.Thakur et al. (2015), Gurjar (2021). Also a fixed and accurate version of various types of Dirichlet averages was given in a treatise by Carlson. Recently, Meena K; Gurjar M.K. (2020) also found the double Dirichlet average of the 3M parameter multi-index Mittag-Leffler function. In this paper, a study of triple Dirichlet averaging of the Mittag-Leffler function is presented.