In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where the
total population was subdivided into nine disjoint compartments, namely, Susceptible(S), Vaccinated with the first dose(V1), Vaccinated with the second dose(V2), Exposed (E), Asymptomatic infectious (I), Symptomatic infectious (I), Quarantine (Q), Hospitalized (H) and Recovered (R). We computed a reproduction parameter, Rv, using the next generation matrix. Analytical and numerical approach is used to investigate the results. In the analytical study of the model: we showed the local and global stability of disease-free equilibrium, the existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium and conducted sensitivity analysis of the model. From these analysis, we found that the disease-free equilibrium is globally asymptotically stable for Rv < 1 and unstable for Rv > 1. A locally stable endemic equilibrium exists for Rv > 1, which shows persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 01, 2021 to January 31, 2022. The unknown parameters are estimated using the least square method with built-in MATLAB function 'lsqcurvefit'. Finally, we performed different simulations using MATLAB and predicted the vaccine dose that will be administered at the end of two years. From the simulation results, we found that it is important to reduce the transmission rate, infectivity factor of asymptomatic cases and increase the vaccination rate, quarantine rate to control the disease transmission. Predictions show that the vaccination rate has to be increased from the current rate to achieve a reasonable vaccination coverage in the next two years.