Free-running diode lasers cannot meet the demands for the line width in the applications due to their broad line width such as Raman scattering and so on. Therefore, it is quite necessary to develop diode lasers with narrow line width, steady wavelength. A reflective holographic grating is taken as a line width narrowing component, and a 405 nm diode laser with external cavity in Littrow configuration is studied. As the introduction of the reflective holographic grating, a coupled external cavity is built between the surface of the grating and the emitting surface of the diode laser, and it improved the line width performance of 450 nm diode laser to a large extent. The experiment results show that, by adding the 2400 line/mm reflective holographic grating, the threshold current of the diode laser is reduced from 31 mA to 22 mA, and line width is reduced form 1 nm to 0.03 nm of free-running, and narrow line width output is realized. A 28 mW output power of the narrow line width laser is got at 100 mA which is 31.7 percent to the power of the free-running diode laser. Besides, by changing the angle of the reflective holographic grating, continuous wavelength tuning of 3.5 nm is realized in a large tuning range of injection current.