Economic growth around the world has not been equal for a long time. Some economics grow faster while others grow slower. But economists have predicted that the slower growing economics will eventually converge with the faster growing economy as some point in the future. This is known as the convergence hypothesis. In this study, we test this hypothesis for Ghana and the Western Europeans countries with UK been a proxy for these countries, using time series data to determine whether or not it holds. We determine how fast or slow this convergence process is by using the returns to scale concept on Ghana’s economy and latter account for factor that determines economic growth in sectors. The study supported the null hypothesis of convergence i.e. Ghana is catching up with the Western European countries. The study also shown that Ghana growth accounting exhibit decreasing returns meaning convergence is relatively slow and also signifies that Ghana is not on a balanced growth path (this refers to the simultaneous, coordinated expansion of several sectors of the economy). The study showed a negative relationship between GDP and labour both in the long run and short run relationship. Again the study showed a positive relationship between GDP and capital, Agric and Industrial sector. Lastly, the study showed a negative relationship between GDP and AID and Service in the long run and positive relationship in the short run.