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 ( The distribution of Q_m values versus epicentral distance and depth show that Q_m values linearly increase with increasing of epicentral distance and depth, and Q_m values is clearly independent of earthquakes magnitude; ( In the different depth ranges, Q_m 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 Q_m residual with time anomaly appears about 2.5 years before the Chi-Chi earthquake; ( A comparison of Q_m residual for different depth range between SML and ALS stations show that the level of stress has vertical and lateral difference; ( The area near observation station with both anomalously increasing and decreasing averaged Q_m 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.