This paper studies the stability and hidden dynamics of the nonlinear hydro-turbine governing system with an output limiting link. A new six-dimensional system, which exhibits some hidden attractors, is proposed in this work. The parameter switching algorithm is used to numerically study the dynamic behaviors of the system. Moreover,it is investigated that for some parameters the system with a stable equilibrium point can generate strange hidden attractors. A self-excited attractor is also recognized with the change of its parameters. In addition, numerical simulations are carried out to analyze the dynamic behaviors of the proposed system using the Lyapunov exponential spectrums, Lyapunov dimensions, bifurcation diagrams, phase space orbits, and basins of attraction. Consequently, the findings of this work show that the basins of hidden attractors are tiny for which the standard computational procedure for localization is unavailable. These simulation results help to have better understanding of hidden chaotic attractors in higher-dimensional dynamical systems.It is also of great significance to reveal chaotic oscillations such as uncontrolled speed adjustment in the operation of hydropower station due to small changes in initial values.