I study Stackelberg–Nash equilibrium and optimal structure for social welfare in the hierarchical continuous Public Goods game. There can be multiple leaders, followers or levels and the leaders are assumed to take linear strategies with respect to the followers’ actions. Explicit forms of Stackelberg–Nash equilibriums of the game under different structures are solved from which social welfare index emerges with good properties. Based on these the optimal 2-level structure for any given population is proved and constructed in steps less than the population size. Moreover, equilibrium under the simplest three-level structure is computed, which implies a bound of hierarchy for theoretical analysis. Results in this paper are rigorous and show interesting phenomena in hierarchical games, which may help decision-making in practice especially in hierarchical systems