  A spherical three-distance set is a finite collection $X$ of unit vectors in
$\mathbb{R}^{n}$ such that for each pair of distinct vectors has three inner
product values. We use the semidefinite programming method to improve the upper
bounds of spherical three-distance sets for several dimensions. We obtain
better bounds in $\mathbb{R}^7$, $\mathbb{R}^{20}$, $\mathbb{R}^{21}$,
$\mathbb{R}^{23}$, $\mathbb{R}^{24}$ and $\mathbb{R}^{25}$. In particular, we
prove that maximum size of spherical three-distance sets is $2300$ in $\mathbb
R^{23}$.
