Past investigations have been done against the sun powered atmosphere relationship and discovered huge comprehension between them. Our goal is to comprehend the sun based atmosphere progress with the assistance of Markov chain lattices. In that association we utilized solar (CI) and climate(ENSO) dataset from 1950 to 2016. All through the period atmosphere information are conveyed into El Nino, La Nino and non-active(ENSO) occasions and discovered solid connection with related CI information. The critical solid 2-dimensional correlation supported connection between El Nino and non-active(ENSO) with related CI networks (0.9865 and 0.8358) separately. So additionally, both El Nino and non-active(ENSO) with contrasting CI shows the higher number of visits in state 3 while La Nino shows a higher number of visits in state 1. Our examination shows the Markov cycle and embraced the main request Markov chain property for CI, El-Nino, La Nina and Non-active(ENSO) boundaries. The obtained results transitional probabilities of climate events with solar activity may be helpful to understand the future variation of events chances using Markov technique.