This study investigates the convergence hypothesis in crop yield of three major kinds of cereal in the world in terms of output production and cereal grain consumption namely rice, wheat and maize during the period 1961 to 2016 across the countries using the conventional analysis of convergence based on modern time series analysis. This has been done first by applying the conventional indicator namely standard deviation. This conventional sigma convergence indicator shows an absence of convergence for all the three crops showing a upward or no trend, thus the paper finds that rice and wheat yield gaps remain on average constant during years, and the maize yield gaps tend to increase. The paper also analyzes the anatomy of those patterns obtained in terms of the evolution of crop yield distribution and club convergence using Markov transition dynamics.