On the base of micro-earthquake seismogram records of Lanzhou temporary digital micro-earth- quake network, and a presumed trilinear geometrical spreading model, the inelastic attenuation Q value is investigated by using genetic algorithm and the method proposed by Atkinson. The frequency-dependent of inelastic attenuation Q value in Lanzhou City and adjacent regions is estimated as Q （f） = 45. 1f1.488. And the result is discussed and analyzed with the results from other regions.