Solid Oxide Fuel Cell (SOFC) systems are subject to operational constraints on state variables, such as fuel cell temperature and pressure. In this research, considerations for optimal operation, which minimizes start-up time while satisfying various restrictions, were derived for SOFC systems. The simultaneous approach by which both state variables and control variables are converted to discrete points in the time domain was applied to the dynamic optimization problem of SOFC systems. Through the conversion, the optimization problem was reformulated as an NLP problem, which was solved using the reduced Hessian successive quadratic programming technique. The optimal operations of manipulated variables were derived to minimize start-up time while satisfying all restrictions, such as the difference in SOFC inlet temperatures, pressures, the rate of temperature change, and the highest temperatures. Furthermore, the design variable of SOFC systems was also optimized to achieve the theoretical minimum start-up time.