With the recent trend in the spread of coronavirus disease 2019 (Covid-19), there is a need for an accurate approximate analytical solution from which several intrinsic features of COVID-19 dynamics can be extracted. This study proposes a time-fractional model for the SEIR COVID-19 mathematical model to predict the trend of COVID-19 epidemic in China. The efficient approximate analytical solution of multistage optimal homotopy asymptotic method (MOHAM) is used to solve the model for a closed-form series solution and mathematical representation of COVID-19 model which is indeed a field where MOHAM has not been applied. The equilibrium points and basic reproduction number are obtained and the local stability analysis is carried out on the model. The behaviour of the pandemic is studied based on the data obtained from the World Health Organization. We show on tables and graphs the performance, behaviour, and mathematical representation of the various fractional-order of the model. The study aimed to expand the application areas of fractional-order analysis. The results indicate that the infected class decreases gradually until 14 October 2021, and it will still decrease slightly if people are being vaccinated. Lastly, we carried out the implementation using Maple software 2021a.