The continuous increase of pollutants and fine particulates is mainly caused by cars circulating worldwide. Therefore, it is necessary to replace internal combustion engines with the cleanest electric motors. The short term solution is represented by Hybrid Electric Vehicles (HEVs) due to its environmental and efficiency characteristics. In the present paper a dynamic feed-forward mathematical model for a hybrid vehicle performance analysis is proposed. Torque and power, pollutant emission, fuel consumption, battery pack state of charge, as well as speed and acceleration have been evaluated by means of simulation of United State and Japanese standard driving cycles. In order to carry out simulations on a real hybrid configuration, the model has been based on the powertrain installed on the Toyota Prius (Toyota Hybrid System - THS). A mathematical sub-model of each vehicle component has been implemented to simulate the real vehicle behavior in all possible running conditions. To do so, a rule-based control strategy was also implemented to manage the energy flows during vehicle motions taking into account battery pack state of charge, vehicle speed, engine and motor torques, as well as power generation in regenerative breaking condition. In order to assess the effectiveness and accuracy of the implemented mathematical model, different simulations on standard driving cycles have been carried out, and results have been compared with experimental data found in scientific literature. The comparison shows a well evident agreement between simulated and experimental data in different running conditions. Furthermore, in an acceleration test from 0 km/h to 100 km/h, the response of the simulated vehicle has been evaluated, and results showed a good agreement between simulated and experimental data. The developed mathematical model is a powerful tool to study the dynamics of powertrain system and the interaction between components. It is also possible to try out new control strategies able to reduce fuel consumption and pollutants emissions maintaining at the same time the required performance.