There is a growing interest on narrow vehicles which can partially solve the parking, congestion and pollution issues associated with urban transportation. A novel narrow vehicle, UW-Car, which is based on a mobile wheeled inverted pendulum (MWIP) platform and a movable seat is proposed in the paper. The three dimensional dynamic model of the underactuated system running on the flat ground is derived by using Lagrange's motion equation. Because of the strong nonlinearity of the UW-Car system, a sliding mode control (SMC) scheme is chosen to ensure the state variables converge to desired values. The velocity control of UW-Car is discussed in this paper. By using the proposed controller, a UW-Car can move at a desired velocity and tracking a given yaw angle velocity while keeping the seat to be always upright. Numerical simulations are provided to verify and illustrate the effectiveness of proposed approaches.