In the conventional seawater desalination hydropower cogeneration mode, issues such as condenser cold source loss and energy cascade waste arise. To address these issues, a new process, referred to as hydropower symbiosis, has been developed for seawater desalination. This process utilizes low calorific value exhaust steam from steam turbine power generation as the heat source for desalination. It makes full use of low-calorific-value blast furnace gas from steel mills to improve the efficiency of the power generation system and utilizes previously wasted energy in the form of waste gas steam for seawater desalination. To achieve collaborative control of water and power cogeneration in the new hydropower symbiosis system, this paper presents a control method based on Stair-like Generalized Predictive Control (SGPC). The key coupling parameter of the hydropower symbiosis system, which is the exhaust steam flow, is controlled to ensure synergy in the system. Firstly, the parameters of the hydropower co-generation system are recognized online based on the actual operation data to correct the system parameters under the change of working conditions. Then, the future output of controlled spent steam flow is predicted based on the CARIMA model, which is easy to identify online, providing a reference or the optimization of the control quantity, i.e., the pumping valve opening. Finally, based on the predicted value of spent steam flow, the optimal sequence of pumping valve openings is determined in real-time on a rolling basis to enhance the stability of spent steam flow control under perturbation and variable operating conditions. The stability and effectiveness of the proposed control method are demonstrated through simulation experiments and validated by the application in a seawater desalination project in the steel plant. Production control data from three months of continuous system operation indicate that the method effectively manages variations in blast furnace gas calorific value and steam pipe network pressure fluctuations while maintaining stable control capabilities. It ensures efficient water production under various conditions and meets power generation requirements, ensuring stable and reliable system operation. This method also holds valuable reference significance for similar problem research and engineering applications.