We study the sample path properties of a generalized fractional Brownian motion (GFBM) introduced by Guodong Pang and Murad S. Taqqu (2019). More precisely, we establish the exact uniform modulus of continuity, small ball probabilities, Chung's LIL and Strassen's local LIL for GFMBM. Our results show that the local regularity properties away from the origin and fractal properties of GFBM are determined by the index $\alpha +\frac1 2$, instead of the self-similarity index $H$. This talk is based on joint works with Prof. Yimin Xiao.