A total of 3 171 seismic records with moment magnitude of 3.5-4.5 collected from the Tianshan area were selected in this paper. Using the microgenetic algorithm and by calculating the Fourier amplitude spectrum of the S-wave velocity, five regional crustal medium parameters were obtained: the stress drop Δσ was 182.06 bar, the quality factor parameter Q₀ was 444.20, the η value was 0.35, and the geometric attenuation parameters R₁ and R₂ were 74.30 and 106.59 km, respectively. Based on the five parameters, the Fourier spectrum of acceleration was calculated. Combined with the random phase spectrum, the time history of ground motion with a certain magnitude and epicentral distance was also obtained. Then, the peak acceleration attenuation relationship of regional ground motion was established. Results show that the attenuation relations of far-field ground motions with moment magnitudes of 5 and 6 are in good agreement with the records of strong ground motions. Among the five selected empirical attenuation relationships, the results for the ground motion with a moment magnitude of 5 are the best for its average value, and the standard deviation is the smallest. The far-field results for the attenuation relationship of ground motion with a moment magnitude of 7 are higher than most strong ground motion records.