Six high-resolution TiO-band image sequences from the New Vacuum Solar Telescope (NVST) are used to investigate the properties of intergranular bright points (igBPs). We detect the igBPs using a Laplacian and morphological dilation algorithm (LMD) and track them using a three-dimensional segmentation algorithm automatically, and then investigate the morphologic, photometric and dynamic properties of igBPs, in terms of equivalent diameter, the intensity contrast, lifetime, horizontal velocity, diffusion index, motion range and motion type. The statistical results confirm the previous studies based on G-band or TiO-band igBPs from the other telescopes. It illustrates that the TiO data from the NVST have a stable and reliable quality, which are suitable for studying the igBPs. In addition, our method is feasible to detect and track the igBPs in the TiO data from the NVST. With the aid of the vector magnetograms obtained from the Solar Dynamics Observatory /Helioseismic and Magnetic Imager, the properties of igBPs are found to be influenced by their embedded magnetic environments strongly. The area coverage, the size and the intensity contrast values of igBPs are generally larger in the regions with higher magnetic flux. However, the dynamics of igBPs, including the horizontal velocity, the diffusion index, the ratio of motion range and the index of motion type are generally larger in the regions with lower magnetic flux. It suggests that the absence of strong magnetic fields in the medium makes it possible for the igBPs to look smaller and weaker, diffuse faster, move faster and further in a straighter path.