Let \(\{u_j:j\ge 1\}\) be an orthonormal basis of Hecke-Maass cusp forms for \(SL_2(\mathbb {Z})\) with Laplace eigenvalue \(\frac{1}{4}+t_{j}^{2}\) . For each \(u_j\) , we have the automorphic symmetric square L-function \(L\left( s,\text{ sym}^{2} u_j\right) \) . In this paper, we establish a sharp bound for the third moment of the central values \(L\left( \frac{1}{2},\text{ sym}^{2} u_j\right) \) in short intervals. Specifically, we show that the estimate \(\begin{aligned} \sum _{|t_j-T|\le \Delta }L\left( \frac{1}{2},\operatorname {sym}^2u_j\right) ^3\ll T^{1+\epsilon }\Delta \end{aligned}\) holds for \(T^{\frac{18}{19}+\epsilon }\le \Delta \le T^{1-\epsilon }\) .
