The energy consumption and CO2 emission of urban vehicles are highly dependent on their operation. Vehicle models can be used for optimizing driving strategy for emission reduction. This paper proposes a novel vehicle model of a one-seat electric vehicle dedicated for Shell Eco-marathon (SEM), the most famous and largest race of energy efficient vehicles. The available vehicle dynamical formulas cannot be directly used to describe the characteristics of lightweight vehicles. In the current work, a novel grey-box vehicle model has been introduced, based on measurement scenarios. The whole model has been elaborated in MATLAB Simulink environment, where individual subassemblies were defined for driving resistance model, powertrain model, and the racetrack characteristics. The resistance force model manages the forces in straight line moving and also takes the effect of cornering into account. Based on test bench measurements the complete efficiency map of the drivetrain was created and implemented into the vehicle model. The presented vehicle model is suitable for driving strategy optimization. By optimizing this model, 7.1 % energy savings have been achieved compared to best human driven lap. Driving strategy optimization will be essential, especially for autonomous vehicles, expressing the importance of the presented results in the future.