We propose a Leaky-Wave Antenna (LWA) based on one-way yttrium-iron-garnet (YIG)-air-metal waveguide. We first analyze the dispersion of the LWA, showing the one-way feature and the radiation loss. Owing to the unique one-way dispersive property, the beam radiated from the LWA can have very narrow beam width, at the same time having large scanning angle. The main beam angle obtained by full-wave simulation is consistent with our theoretical prediction with the aid of the dispersion. For a given frequency, we can realize continuous beam scanning by varying the magnetic field, where the 3 dB beam width is much narrower than previously demonstrated. Our results pave a new way to realize continuous angle scanning at a fix frequency for modern communications.