  Let $[\, \cdot\,]$ be the floor function. In this paper, we show that when
$1<c<37/36$, then every sufficiently large positive integer $N$ can be
represented in the form \begin{equation*} N=[p^c_1]+[p^c_2]+[p^c_3]\,,
\end{equation*} where $p_1,p_2,p_3$ are primes close to squares.
