A convenient and efficient rural road network helps to develop the rural economy and promote national rural revitalization. This paper systematically analyzes the role of rural road infrastructure construction on economic growth from a theoretical perspective. Simultaneously, it employs a computer algorithm based on vector autoregression to construct an econometric model. Based on this theoretical analysis empirically examines the relationship between rural infrastructure construction and economic development. It collects data from a city’s rural area from 2000 to 2020 as a research sample and conducts a series of analyses, including VAR model estimation, impulse response, and variance decomposition. The results show that rural road infrastructure construction has a significant impact on economic growth, with coefficients of −0.288 and 0.356 for lags 1 and 2. The construction of rural road infrastructure is responsible for more than 90% of the variation in economic growth, whereas the opposite is about 10%. Therefore, rural road infrastructure development does not have a significant effect on economic growth in the short term but has a significant effect in the medium and long term.