Because of the large linewidth, dither and drift , the commercial diode laser cannot meet the requirement of the experiments of laser cooling and elaborating measurement of a single calcium ion trapped in an ion trap. In this paper, a tunable Littrow-configuration external cavity diode laser (ECDL) is constructed. The free spectral range of the laser cavity is 1.5 GHz. By adjusting the angle of the grating, wavelength of the laser can be adjusted from 775 nm to 785 nm. Linewidth of the laser is less than 2.5 MHz, dithering of the laser is about 3～4 MHz, and drift of the laser is about 50 MHz within 30 minutes. These indexes are better than those commercial DL100 lasers. The laser is the base that will construct the next 397 nm and 866 nm lasers for laser cooling and elaborating measurement of a single calcium.