Earthquake source mechanisms are used to determine local geological characteristics and hazard mitigation. There are several approaches to determine the mechanism of earthquake. In this paper, the relative time of the rupture duration is applied to determine rupture directivity. In determining rupture directivity, the Levenberg-Marquardt (LM) method is proposed to solve the inversion problem. To test the reliability of this method, teleseismic data with an epicentral distance of 40o from the Philippine earthquake on 15 December 2019 6.8, which had a good seismic station distribution with a total of 35 stations, is used. Telesismic data from each station is filtered in the range of 0.25 to 1 Hz to obtain an accurate rupture duration. Furthermore, the rupture duration data set was inverted using the LM method to obtain the direction of earthquake rupture. The results obtained by the curve fitting using the LM method had a good agreement between the observed data and the calculated data. From the curve fitting results, the rupture propagated in the NW direction with azimuth 320.60o ± 2.30o, and this had the same results from previous studies. Therefore, from rupture directivity, the actual fault plane of this earthquake was NP1 which had a strike/dip/rake value of 321o/75o/13o, respectively. The results indicate that the Philippines earthquake of 15 December 2019 had the SE-NW fault orientation, which is part of the Cotabato fault system. The implication of this research is for a preliminary study related to the characteristics of earthquake rupture in areas that have a high level of seismicity. Thus, local residents can avoid areas where ruptures propagate when carrying out earthquake mitigation.