The phenomenal growth in mobile data traffic calls for a drastic increase in mobile network capacity beyond current 3G/4G networks. In this paper, we propose a millimeter wave mobile broadband (MMB) system for the next generation mobile communication system (5G). MMB taps into the vast spectrum in 3-300 GHz range to meet this growing demand. We reason why the millimeter wave spectrum is suitable for mobile broadband applications. We discuss the unique advantages of millimeter waves such as spectrum availability and large beamforming gain in small form factors. We also describe a practical MMB system design capable of providing Gb/s data rates at distances up to 500 meters and supports mobility up to 350 km/h. By means of system simulations, we show that a basic MMB system is capable of delivering an average cell throughput and cell-edge throughput performances that is 10-100 times better than the current 20MHz LTE-Advanced systems.