  The Tribonacci sequence $\mathbb{T}$ is the fixed point of the substitution
$\sigma(a,b,c)=(ab,ac,a)$. In this note, we get the explicit expressions of all
squares, and then establish the tree structure of the positions of repeated
squares in $\mathbb{T}$, called square trees. Using the square trees, we give a
fast algorithm for counting the number of repeated squares in $\mathbb{T}[1,n]$
for all $n$, where $\mathbb{T}[1,n]$ is the prefix of $\mathbb{T}$ of length
$n$. Moreover we get explicit expressions for some special $n$ such as $n=t_m$
(the Tribonacci number) etc.
