The governing equations of the moist air of a solar updraft power plant (SUPP) are derived with the consideration of the condensation occurring in the tower based on the compressible fluid model. The expression of the pressure potential of a large-scale SUPP containing no integral is also established while the condensation of water vapor exists in the tower. Based on the developed mathematical model, the transient state simulation of the performance of the SUPP under Wuhan climate conditions is carried out. Three scenarios that incorporate different treatments of the humidity of the ambient air, i.e. dry ambient, moist ambient without condensation in the plant, moist ambient with condensation in the plant, are simulated on a typical day in the summer of Wuhan. The consideration of moisture and condensation produces more power generation than the other scenarios. However, the peak daily power output is obtained for the dry ambient. With the increase in the relative humidity of the ambient air, the total power generation decreases first and then increases while the condensation starts occurring. The power output also becomes smoother with higher relative humidity. The profile of power generated from the reference SUPP in Sishen, South Africa with abundant solar radiation and that in Wuhan with heavy moisture are compared.