Effective energy infrastructure investment strategy could optimize the reallocation of energy resources, promote the coordinated development across regions, and narrow the regional development inequality. This paper investigates how the energy infrastructure investment could affect the regional economic growth, based on the evidence of China’s power grid during 2000-2014. The “Effective Cost Index” (ECI) is formulated to measure the development degree of power grid infrastructure (PGI) at first. After that, the economic growth convergence model is adopted to analyze the impact of PGI on regional economic convergence by the method of system GMM. Moreover, different PGI investment scenarios are simulated to discuss what the optimal investment distribution is. The results present that the ECI can impact the regional economic growth negatively, and the PGI investment may generate higher marginal benefits for the less developed inland areas than the developed coastal areas. In China, the most effective way to narrow regional inequality is to distribute the PGI investment to the central hub provinces.