We study the minimax settings of binary classification with F-score under the $β$-smoothness assumptions on the regression function $η(x) = \mathbb{P}(Y = 1|X = x)$ for $x \in \mathbb{R}^d$. We propose a classification procedure which under the $α$-margin assumption achieves the rate $O(n^{--(1+α)β/(2β+d)})$ for the excess F-score. In this context, the Bayes optimal classifier for the F-score can be obtained by thresholding the aforementioned regression function $η$ on some level $θ^*$ to be estimated. The proposed procedure is performed in a semi-supervised manner, that is, for the estimation of the regression function we use a labeled dataset of size $n \in \mathbb{N}$ and for the estimation of the optimal threshold $θ^*$ we use an unlabeled dataset of size $N \in \mathbb{N}$. Interestingly, the value of $N \in \mathbb{N}$ does not affect the rate of convergence, which indicates that it is "harder" to estimate the regression function $η$ than the optimal threshold $θ^*$. This further implies that the binary classification with F-score behaves similarly to the standard settings of binary classification. Finally, we show that the rates achieved by the proposed procedure are optimal in the minimax sense up to a constant factor.