The article discusses conditional β-convergence in 126 countries around the world in 1975-2003. The authors offer a theoretical model to explain the essence of convergence. Unlike in most empirical studies, the authors assume that convergence, or the relationship between the rate of economic growth and the initial level of GDP, is not constant but changes over time. The model was constructed on the basis of panel data, using the Fixed Effects estimator and the Generalized Method of Moments estimator developed by Arellano and Bond. The results of the evaluation confirm the existence of β-convergence, which is much faster than suggested by most empirical studies. When per capita GDP is 1% higher, the rate of growth falls by 0.20-0.22 percentage points on average. The β-convergence indicator ranges from 22% to 25%. By assuming that convergence is not constant, the authors proved that there is a strong relationship between the initial level of GDP and the rate of economic growth. This shows that their assumption was fully justified as the main hypothesis of the analysis.