This paper brings attention to a new nonlinear mathematical model of a hydro-turbine governing system with a surge tank. The nonlinear mathematical model, which is described by state-space equations, is composed of Francis turbine system, electrical generator system, conduit system and governor system. Furthermore, the nonlinear dynamical behaviors of the system with different parameters are studied exhaustively including bifurcation diagrams, time waveforms, phase orbits, Poincare maps, spectrograms and power spectrums. Fortunately, some interesting phenomenons are found from numerical simulation results. More important, all of the above analyses supply some theory bases for designing and running of a hydro-turbine governing system. (C) 2013 Elsevier Inc. All rights reserved.