The new inversion algorithm developed based on the recent progress in the nonlinear programming study by us is used to invert the earthquake source process of Chi Chi earthquake Mw7.6, 20 Semptember,1999, Taiwan. A curve fault model is constructed in our inversion to make the fault model close to the real rupturing fault to reduce the influence from the discrepancy 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 main faulting occurred between 6th to 21st second after the start of the ruptures and the high slip area were mainly located at the northern segment of the fault. (2) The slip was dominated by thrust faulting. 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 paper was 7.76×1020 NM, which was a slightly bigger than those inverted by USGS and Harvard. (3) A clear nucleation step existed in the source faulting process and it lasted about 6 seconds. The moment release rate accelerated obviously at the end of the nucleation step. The faulting started from the southern segment and mainly occurred at the northern segment after 10 seconds. At the end of this paper, we analyzed the reliability of the inver- sion result via comparing with the GPS observations and discussed its scientific signification. The new inversion algorithm developed based on the recent progress in the nonlinear programming study by us is used to invert the earthquake source process of Chi Chi earthquake Mw 7.6, 20 Semptember, 1999, Taiwan. A curve fault model is constructed in our inversion to make the fault model close to the real rupturing fault to reduce the influence from the discrepancy 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 main faulting occurred between 6th to 21st second after the start of the ruptures and the high slip area were mainly located at the northern segment of the fault. (2) The slip was dominated by thrust faulting. 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 paper was 7.76 × 1020 NM, which was a slightly bigger than tho se inverted by USGS and Harvard. (3) A clear nucleation step existed in the source faulting process and it lasted about 6 seconds. The moment release rate accelerated obviously at the end of the nucleation step. The faulting started from the southern segment and mainly occurred at the northern segment after 10 seconds. At the end of this paper, we analyzed the reliability of the inver- sion result via comparison with the GPS observations and discussed its scientific signification.