Dissipative Hamilton control problem for the speed and tension system of the reversible cold strip rolling mill is studied based on the immersion and invariance(I&I) adaptive method and the nonlinear disturbance observer(NDO). Firstly, the I&I adaptive method is used to estimate the perturbation parameters of the system. Next, the dissipative Hamilton model of the speed and tension outside loop is built after pre-feedback control, and dissipative Hamilton controllers are designed by utilizing the interconnection and damping assignment, and energy shaping method. Further more, external disturbances in the system current inside loop are observed by NDOs, and the observed values are introduced into the integral sliding mode controllers for compensation. Finally, a simulation is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill, and results show the effectiveness of the proposed control strategy.