We present results of 2 hr non-interrupted observations of solar granulation obtained under excellent seeing conditions with the largest aperture ground-based solar telescope-the New Solar Telescope (NST)-of Big Bear Solar Observatory. Observations were performed with adaptive optics correction using a broadband TiO filter in the 705.7 nm spectral line with a time cadence of 10 s and a pixel size of 0 ''.0375. Photospheric bright points (BPs) were detected and tracked. We find that the BPs detected in NST images are cospatial with those visible in Hinode/SOT G-band images. In cases where Hinode/SOT detects one large BP, NST detects several separated BPs. Extended filigree features are clearly fragmented into separate BPs in NST images. The distribution function of BP sizes extends to the diffraction limit of NST (77 km) without saturation and corresponds to a log-normal distribution. The lifetime distribution function follows a log-normal approximation for all BPs with lifetime exceeding 100 s. A majority of BPs are transient events reflecting the strong dynamics of the quiet Sun: 98.6% of BPs live less than 120 s. The longest registered lifetime was 44 minutes. The size and maximum intensity of BPs were found to be proportional to their lifetimes.