  Let $\{X_n\}_n$ be a sequence of freely independent, identically distributed
non-commutative random variables. Consider a sequence $\{W_n\}_n$ of the
renormalized spectral maximum of random variables $X_1,\cdots, X_n$. It is
known that the renormalized spectral maximum $W_n$ converges to the free
extreme value distribution under certain conditions on the distribution
function. In this paper, we provide a rate of convergence in the Kolmogorov
distance between a distribution function of $W_n$ and the free extreme value
distribution.
