G-band bright points (GBPs) are regarded as good manifestations of magnetic flux concentrations. We aim to investigate the relation between the dynamic properties of GBPs and their longitudinal magnetic field strengths. High spatial and temporal resolution observations were recorded simultaneously with G-band filtergrams and Narrow-band Filter Imager (NFI) Stokes and images with Hinode/Solar Optical Telescope. The GBPs are automatically identified and tracked in the G-band images, and the corresponding longitudinal magnetic field strength of each GBP is extracted from the calibrated NFI magnetograms by a point-to-point method. After categorizing the GBPs into five groups by their longitudinal magnetic field strengths, we analyzed the dynamics of each group of GBPs. The results suggest that with increasing longitudinal magnetic field strengths of GBPs correspond to a decrease in their horizontal velocities and motion ranges as well as by showing more complex motion paths. This suggests that magnetic elements showing weaker magnetic field strengths move faster and farther along straighter paths, while stronger elements move more slowly in more erratic paths within a smaller region. The dynamic behaviors of GBPs with different longitudinal magnetic field strengths can be explained by that the stronger flux concentrations withstand the convective flows much better than weaker ones.