The mathematical modelling of the Coronavirus disease (COVID-19) outbreak in India is done by using the logistic growth model and the Susceptible-Infectious-Recovered (SIR) framework. Karnataka, Kerala and Maharashtra, three states of India, are selected based on the pattern of the disease spread and the prominence in being affected in India. The parameters of the models are estimated by utilizing real-time data. The models predict the ending of the pandemic in these states and estimate the number of people that would be affected under the prevailing conditions. The models classify the pandemic into five stages based on the nature of the infection growth rate. According to the estimates of the models it can be concluded that Kerala is in a stable situation whereas the pandemic is still growing in Karnataka and Maharashtra. The infection rate of Karnataka and Kerala are lesser than 5% and reveal a downward trend. On the other hand, the infection rate and the high predicted number of infectives in Maharashtra calls for more preventive measures to be imposed in Maharashtra to control the disease spread.