The launch of high-quality development has become an inevitable choice at this stage to cope with the new international situation, transform and improve the industrial structure, and pursue the Chinese dream. The aim of this study was to scientifically measure the stage of high-quality economic development and analyze the role of human capital in such development. In this paper, we construct an indicator system based on innovation, sharing, green economy, opening, and coordination. The spatial distribution of high-quality economic development is evaluated by using the genetic algorithm–projection pursuit model, and its impact is studied by using the spatial panel quantile regression method. The results show that the development level of regional economic quality is increasing annually, revealing a situation in which the east is leading, the center is rising, and the west is catching up. Among the factors affecting high-quality economic development, in this region, it has a positive inverted U-shaped influence on neighboring regions. Regarding quality improvement, the impact of human capital presents a U-shaped curve. In other words, it benefits from the catch-up effect of the lower-level provinces and the first mover advantage of the higher-level provinces. Based on this, corresponding countermeasures are put forward.