The ongoing novel coronavirus epidemic was announced a pandemic by the World Health Organization on March 11, 2020, and the Government of India declared a nationwide lockdown on March 25, 2020 to prevent community transmission of the coronavirus disease (COVID)-19. Due to the absence of specific antivirals or vaccine, mathematical modeling plays an important role in better understanding the disease dynamics and in designing strategies to control the rapidly spreading infectious disease. In our study, we developed a new compartmental model that explains the transmission dynamics of COVID-19. We calibrated our proposed model with daily COVID-19 data for four Indian states, namely, Jharkhand, Gujarat, Andhra Pradesh, and Chandigarh. We study the qualitative properties of the model, including feasible equilibria and their stability with respect to the basic reproduction number R0. The disease-free equilibrium becomes stable and the endemic equilibrium becomes unstable when the recovery rate of infected individuals increases, but if the disease transmission rate remains higher, then the endemic equilibrium always remains stable. For the estimated model parameters, R0>1 for all four states, which suggests the significant outbreak of COVID-19. Short-time prediction shows the increasing trend of daily and cumulative cases of COVID-19 for the four states of India.