According to the local fractal feature in an astronomical spectrum, the data in the spectrum were coded in three bands 400~510, 600~700 and 780~900 nm. In the present paper, using the position of the matching data block and the minimum matching error, the fractal coding method was used to recognize the subtypes of astronomical spectra for the first time. The experimental results show that the fractal coding method has certain noise immunity and cannot be affected by the calibration error and the effective curves of LAMOST. The fractal method can effectively recognize the subtype of M stars of LAMOST and SDSS.