The new inversion algorithm developed based on the recent progress in thenonlinear programming study by us is used to invert the earthquake source process of Chi Chiearthquake M_w7.6, 20 Semptember,1999, Taiwan. A curve fault model is constructed in our inversionto make the fault model close to the real rupturing fault to reduce the influence from thediscrepancy between the constructed fault model and the real rupturing fault. The results show that(1) the rupture process of the Chi Chi earthquake source lasted about 32 seconds and the mainfaulting occurred between 6th to 21st second after the start of the ruptures and the high slip areawere mainly located at the northern segment of the fault. (2) The slip was dominated by thrustfaulting. The average rake angle was 64.5°, which was very consistent with those inverted by USGS,Harvard and CWB (Central Weather Bureau of Taiwan). The amount of the moment inverted in this paperwas 7.76x10^(20) NM, which was a slightly bigger than those inverted by USGS and Harvard. (3) Aclear nucleation step existed in the source faulting process and it lasted about 6 seconds. Themoment release rate accelerated obviously at the end of the nucleation step. The faulting startedfrom the southern segment and mainly occurred at the northern segment after 10 seconds. At the endof this paper, we analyzed the reliability of the inversion result via comparing with the GPSobservations and discussed its scientific signification.