Based on the measurement of the arrival time of maxima magnitude from band-pass filtering signals which were determined using a new Morlet wavelet multiple-filter method, we develop a method for measuring intrinsic and attenuative dispersion of the first cycle direct P-wave. We determine relative group delays of spectral components of direct P-waves for 984 ray paths from SML and ALS stations of the Taiwan Central Weather Bureau Seismic Network (CWBSN). Using continuous relaxation model, we deduce a new transfer function that relates intrinsic dispersion to attenuation. Based on the genetic algorithm (GA), we put forward a new inversion procedure for determining which is defined the flat part of quality factor Q(ω) spectrum, τ1 and τ2 parameters. The results indicate that ① The distribution of Qm values versus epicentral distance and depth show that Qm values linearly increase with increasing of epicentral distance and depth, and Qm values is clearly independent of earthquakes magnitude; ② In the different depth ranges, Qm residual show no correlation with variations in epicentral distance. Some significant changes of Qm residual with time is likely caused by pre-seismic stress accumulation, and associated with fluid-filled higher density fractures rock volume in the source area of 1999 Chi-Chi Taiwan earthquake. We confirm that Qm residual with time anomaly appears about 2.5 years before the Chi-Chi earthquake; ③ A comparison of Qm residual for different depth range between SML and ALS stations show that the level of stress has vertical and lateral difference; ④ The area near observation station with both anomalously increasing and decreasing averaged Qm residual is likely an unstable environment for future strong earthquake occurrence. This study demonstrates the capability of direct P-waves dispersion for monitoring attenuation characteristics and its state changes of anelastic medium of the Earth at short propagation distance using seismograms recorded from very small events.