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We prove an optimal Kawamata-Miyaoka type inequality for terminal $\mathbbQ$-Fano threefolds with Fano index $\geq 3$. As an application, we obtain thatany terminal $\mathbb Q$-Fano threefold $X$ satisfies the followingKawamata-Miyaoka type inequality \[ c_1(X)^3 < 3c_2(X)c_1(X). \]

Kawamata-Miyaoka type inequality for canonical $\mathbb Q$-Fano varieties II: terminal $\mathbb Q$-Fano threefolds