In order to further enhance the stability of traffic flow, based on the classical Optimal Velocity Changes with Memory (OVCM) model, a novel car-following model for intelligent connected vehicles based on Multiple Headway Optimal Velocity and Acceleration (MHOVA) was proposed. Firstly, the optimal velocity change of k leading cars was introduced with the weight γ, as well as the acceleration of the nearest leading car was considered with the weight ω. Then, the critical stability conditions of traffic flow were obtained based on the proposed model and by the linear stability analysis. Finally, the numerical simulations and analyses were carried out on the parameters such as velocity and headway of the fleet with disturbance by Matlab. Simulation results show that, in the simulation of the starting and stopping processes of the fleet, the proposed model reduces the time to obtain the stable state of the fleet compared to OVCM does, in the simulation of a disturbance to the fleet on the annular road, if both ω and k are of rationality, the proposed model can perform the less fluctuations in terms of velocity and headway, compared with the Full Velocity Difference (FVD) model, OVCM and the Multiple Headway Optimal Velocity (MHOV) model. Especially when ω is 0.3 and k is 5, the minimum upward and downward fluctuations of vehicle velocity can be 0.67% and 0.47% respectively. Consequently, the proposed model can better absorb traffic disturbance and enhance the driving stability of fleet.