To obtain appropriate source parameters from waveform inversions using near-field strong motion records at only one or two stations, we examined the 1990 Odawara earthquake (M_J5.1) that has been well studied by many researchers. We used strong motion data recorded at two stations in the Kuno area of Odawara City, and released by the Japanese National Working Group on the Effects of Surface Geology on Seismic Motion (JESG). These stations were located at distances of 7-8km from the epicenter. We estimated the seismic moment, strike, dip, and rake of a double-couple point source by applying a grid search technique to the displacement seismograms bandpass-filtered between 2 and 10s. The data from KR1 and KD2 were used for each single-station inversion and for the two-station inversion. The first attempt with no constraint to the unknown parameters yielded reverse-faulting mechanisms similar to those of previous studies. Because the difference in the strike and rake was significant, we investigated the dependence of error between the observed and calculated waveforms on unknown parameters. We found that the strike of the low-dip nodal plane is the most appropriate parameter to be constrained. Constraining the strike within the range of the previous solutions, we carried out one- and two-station inversions to obtain reasonable source parameters compared with the previous solutions. The agreement between the observed and the synthetic waveforms is satisfactory even for the constrained solution. Moreover, through numerical experiments, we confirmed that constraining the strike could be effective in estimating source parameters of the target event for stations of different azimuth.