A car-following model named total generalized optimal velocity model (TGOVM) was developed with a consideration of an arbitrary number of preceding vehicles before current one based on analyzing the previous models such as optimal velocity model (OVM), generalized OVM (GOVM) and improved GOVM (IGOVM). This model describes the physical phenomena of traffic flow more exactly and realistically than previous models. Also the performance of this model was checked out by simulating the acceleration and de- celeration process for a small delay time. On a single circular lane, the evolution of the traffic congestion was studied for a different number of headways and relative velocities of the preceding vehicles being taken into account. The simulation results show that TGOVM is reasonable and correct.