In this brief note we give an upper bound for $P(τ_u < T)$ with $T>0$, where $τ_u$ is the exit time defined as $τ_u:=\inf \{ t\geq 0 \, : \, X_t\geq u \}$ and $(X_t)_{t\geq 0}$ is the fractional Ornstein-Uhlenbeck processes which satisfies the following stochastic differential equation \begin{equation*} dX_t =-λX_t dt+ εdB_t^H\quad ε>0,\;λ>0 \end{equation*} with $(B_t^H)_{t\geq 0}$ as the fractional brownian motion with parameter of Hurst $H\in ]0,1]$.