We consider a (pure) public goods provision problem with voluntary participation in a quasi-linear economy. We propose a new hybrid solution concept, the free-riding-proof core (FRP-Core), which endogenously determine a contribution group, public good provision level, and its cost-sharing. The definition of the FRP-Core is based on credibility of coalitional deviations. The FRP-Core is always nonempty in public good economy but does not usually achieve global efficiency. The FRP-Core has support from both cooperative and noncooperative games. In particular, it is equivalent to the set of perfectly coalition-proof Nash equilibrium (Bernheim, Peleg and Whinston, 1987 JET) of a dynamic game with participation decision followed by a common agency game. We illustrate the properties of the FRP-Core with an example. We also show that the equilibrium level of public good shrinks to zero as the economy is replicated.