Solid oxide fuel cell (SOFC) plant is considered a most important type in the field of fuel cells, which gives control difficulties such as fuel flow constraints, load disturbance, system nonlinearities, and parameter uncertainties. However, due to these difficulties, the voltage control of SOFC plant is extremely difficult. In this paper, a new intelligent proportional integral-adaptive sliding mode control (iPI-ASMC) with anti-windup compensator is proposed to control the output voltage of SOFC plant to keep up with the rated voltage. The referred iPI-ASMC is made of three sub-components: (i) an extended state observer (ESO)-based-intelligent proportional-integral to estimate the unknown dynamic, (ii) an adaptive sliding mode control is added to compensate the estimation error of unknown dynamic, and (iii) an anti-windup compensator based on back-calculation is used to deal with saturation problem which is caused by input constraints. Moreover, the effectiveness and efficiency of the proposed iPI-ASMC strategy is demonstrated by comparing with some other approaches such as conventional proportional integral-derivative (PID) controller, intelligent proportional-integral (iPI) and fuzzy PID controller. Corresponding simulation results show that the proposed iPI-ASMC approach provides better dynamic responses and outperforms to compared methods in term of settling time, peak overshoots, integral absolute error (IAE), integral square error (ISE), and integral time absolute error (ITAE).