We will study the least square estimator $hat{ heta}_{T,S}$ for the drift parameter ${ heta}$ of the fractional Ornstein-Uhlenbeck sheet which is defined as the solution of the Langevin equation $$X_{t,s}=-{ heta}{int}_{0}^{t}{{int}_{0}^{s};X_{v,u}dvdu+B^{{alpha},{eta}}_{{t,s}}$$, $$(t,;s);{in};[0,;T]{ imes}[0,;S]$$. driven by the fractional Brownian sheet $B^{{alpha},{eta}}$ with Hurst parameters ${alpha}$, ${eta}$ in ($frac{1}{2}$, $frac{5}{8}$). Using the properties of multiple Wiener-It$hat{o}$ integrals we prove that the estimator is strongly consistent for the parameter ${ heta}$. In contrast to the one-dimensional case, the estimator $hat{ heta}_{T,S}$ is not asymptotically normal.