Minimizing the total weight of a stratospheric airship reflects the design object of lowest total cost to a certain extent. To meet the power requirement of payload is the springboard and goal for the conceptual design of the airship. The model of paving solar cells on curved surface and the model of energy-closed loop during day and night were introduced in the parametric modeling of the airship. The particle swarm optimization algorithm was used to optimize the parameters of the outside size. The design object is to find a feasible airship which has minimum total mass and satisfies the constraints with three balances: the diurnal balance between the energy supply and the energy requirement, the balance between mass and buoyancy, and the balance between drag and thrust. The sensitivity of the optimization results with different requirement of payload power and payload specific power was analyzed. The analysis results show that: the total airship weight increases linearly with the payload power; the total airship weight decreases steeply with the payload power density, but the change rate of the total weight also decreases and the total weight tends to be stable. The results of energy system simulation indicate the validity of the conceptual design method, as well as the critical characteristics of the design results.