Free-running diode lasers can not satisfy the demands of spectroscopy applications such as Raman scattering which requires narrow line-width. In order to obtain narrow line-width laser at 405 nm band, external cavity with reflective holographic gratings for blue-violet laser diode (LD) is studied. The spectra of the blue-violet LD with a grating external cavity in Littrow configuration are measured by a high resolution monochromator, and the characteristics of threshold and tuning property are investigated through its output power and spectra. It is found that the threshold current of LD is reduced from 30.0 mA to 19.7 mA or 21.3 mA when the groove density of the grating is 2400 l/mm or 3600 l/mm respectively, and the line-width is suppressed within 0.03 nm in the full scope of injection currents while the line-width of the free running LD is approximately 1nm. Furthermore, tuning ranges of 5.45 nm and 5.33 nm are achieved. These results is helpful for the spectroscopy applications of blue-violet LD.