The theory of absolute convergence states that the growth level of countries initially varies due to the difference in their levels of capital. The second theory of conditional convergence states that each country has a steady state and they converge to their own level of the steady state.The paper focuses on the effect of convergence on China and the resultant financial development and economic growth in this country. Deep-down analysis of the fact that poor countries can catch up to the rich countries through the increase in the average rates of growth has been carried on for a proper understanding of this topic. The investigation of the way in which the financial development and economic growth of China helped it to reach the position equivalent to a developed country is considered for the purpose of review. The Solow swan model and laws of diminishing marginal utility are used to help in the process of interpretation of the topic in a simple and easy manner. The empirical evidence is laid down in the paper along with charts to facilitate the process of understanding.The idea of catch-up-effect or convergence in economics is based on the hypothesis that the per capita income of the poorer economies will tend to grow at a much faster rate than the richer ones. The resultant factor is the convergence of both the economies in terms of the per capita income. The financial functions control the investment and saving decisions, technological innovations and therefore economic growth (Shahbaz, Khan and Tahir, 2013).Classical theories: The Ricardian theory of production and growth are related to the law of variable proportion. The law states that if any factor of production is increased while keeping the other same with no technological changes, there can be an increase in the output but in diminishing rate. This increased output eventually approaches towards zero.