P-wave first motion, an unambiguous physical quantity, is a kind of steady seismic information. When enough data were available, it could be used to ideally determine focal mechanism solutions. The most popular method for employing P-wave first motion to determine focal mechanism solutions is the grid search method. However, when applied to earthquakes with few data points, grid search method still has great uncertainty, although it is believed to be better than the iterative method. By now, no satisfactory settlement has been found, which greatly restricts the application of this method. In this paper, we focus on the improvement of former grid search methods. Firstly, possible solutions are selected by weighted inconsistency ratio. Here, the weighting scheme retains the data-quality weighting factor so as to consider the influence of data quality, omits the weighting factor reflecting the distance between data points and nodal planes for avoiding over-reducing the weights of the observations near nodal planes, and adds another weighting factor which gives more power to sparse data points on the focal sphere for partly canceling out the influence of uneven distribution of the employed data points. Meanwhile, we divide the focal sphere into several roughly equal-square areas, which prevent deviation from real mean solution by artificial concentration of test solutions. We improve our inversion quality by employing jackknife technique, which enlarges the solution set by adding those possible solutions for one observation being ignored. This technique, along with clustering analysis, not only increases the possibility of finding out true solutions, but also makes us comprehend the quality of focal mechanism solutions unambiguously. Finally, we provide a new scheme for evaluating the quality of focal mechanism solutions based on the dispersion of selected solutions as well as the minimum weighted inconsistency ratio.