This paper seeks to investigate the motivations of countries that participate in the One Belt and One Road (B&R) Initiative, a China-led economic development programme with the intention of enhancing regional economic cooperation. We examine the income convergence hypothesis for B&R countries with both linear and nonlinear unit root tests to detect the presence of economic integration over the periods 1960-2016 and 1979-2016. For the B&R countries that are found to show income convergence to China in our income convergence testing, we argue that they tend to have a strong existing economic relationship with China. By contrast, the countries that have relatively weak economic relationships with China tend to show no convergence to China, and they take advantage of the B&R as an opportunity to catch up. Moreover, we find evidence that more countries converge to China's real per capita income for the years after 1978 when China started its transition to a market economy and initiated the open-door policy to embrace globalization. The results suggest that China contributes to a higher degree of income convergence in regional integration.