The trivalent Cayley graph TCn was introduced and investigated in [1], [2]. Though "the diameter" was presented in [2], unfortunately it was not the diameter but an upper bound of it. In this paper, a lower bound of the diameter dia(TCn) of the trivalent Cayley graph TCn is investigated and the formula dia(TCn) = 2n - 2 for n greater than or equal to 3 is established.