To investigate the impact of new digital infrastructures on economic growth, a dynamic general equilibrium model of economic growth was built firstly incorporating the capital stock of new digital infrastructure and its congestion into the aggregate production function. Secondly, the new digital infrastructure capital stocks in provinces of China from 2002 to 2020 were calculated and analyzed. Based on that, a static panel data model and three spatial panel models using provincial panel data for China from 2002 to 2020 were developed to empirically test the impact of the new digital infrastructure on economic growth. Both theoretical and empirical results show that the effects of new digital infrastructure on economic growth change as an “inverted U-shaped”, that is to say, having larger share of new digital infrastructure capital stock does not necessarily mean that it is better; The construction of new digital infrastructure has significant spatial spillover effects, which means that to construct new digital infrastructure in one province not only promotes the local economic growth, but also promotes other provincial economic growth through spatial spillover effects. Solve for the optimal share of infrastructure capital stock at the apex of the “inverted U-shaped” to be 38.66%. At present, the shares of new digital infrastructure capital stock in all provinces of China are below 38.66%, which means that it may increase the outputs per capita of all provinces to increase the share of new digital infrastructure capital stock in one province.