A micro-spectrometer which adopts the holographic concave grating as imaging and dispersing element is introduced in the paper. Using ZEMAX soft ware tools, the optimal design of aberration correction of the concave grating which retains the image quality without sacrificing the resolution is coming up with. The portable micro-spectrometer with F/#4 is developed. During 350nm to 800nm wavelength range, the resolution of this kind of micro-spectrometer is better than 0.5nm. In addition, the diffraction efficiency of the concave grating, which is a very important indicator of the spectrometer and confines the detecting ability to the faintest spectrograph, is calculated by means of the rigorous coupled wave theory of the grating. The relationship between the diffraction efficiency of the concave grating and its profile parameters is discussed, too. The results obtained from these researches provide the necessary guidance in fabrication of the micro-spectrometer.