In this Letter, we introduce an aspiration-induced reconnection mechanism into the spatial public goods game. A player will reconnect to a randomly chosen player if its payoff acquired from the group centered on the neighbor does not exceed the aspiration level. We find that an intermediate aspiration level can best promote cooperation. This optimal phenomenon can be explained by a negative feedback effect, namely, a moderate level of reconnection induced by the intermediate aspiration level induces can change the downfall of cooperators, and then facilitate the fast spreading of cooperation. While insufficient reconnection and excessive reconnection induced by low and high aspiration levels respectively are not conductive to such an effect. Moreover, we find that the intermediate aspiration level can lead to the heterogeneous distribution of degree, which will be beneficial to the evolution of cooperation.