A connected vehicle can get data from the Intelligent Transportation System (ITS). This allows the car to estimate accurate vehicle states (speed, acceleration, instantaneous fuel consumption) and to use traffic information (signal, queue length, shockwave). Traffic information is very important for vehicle driving at urban intersections because traffic information (shock wave, queue length) means the effect of the driver. The fuel optimal speed profile algorithm must contain vehicle and traffic information. This paper proposes fuel optimal speed profile algorithm for the connected vehicle at the intersection. The algorithm uses the model predictive control method (MPC) to reflect traffic information constraints. The constraints change according to the traffic situation(lead vehicle, following vehicle). The algorithm is verified using a microscopic simulation tool (AIMSUN).