Time-dependent quantum transport parameters for graphene nanoribbons (GNR) are calculated by the hierarchical equation of motion (HEOM) method based on the nonequilibrium Green's function (NEGF) theory [Xie et al., J. Chem. Phys. 137, 044113 (2012)]. In this paper, a new initial-state calculation technique is introduced and accelerated by the contour integration for large systems. Some Lorentzian fitting schemes for the self-energy matrices are developed to effectively reduce the number of Lorentzians and maintain good fitting results. With these two developments in HEOM, we have calculated the transient quantum transport parameters in GNR. We find a new type of surface state with delta-function-like density of states in many semi-infinite armchair-type GNR. For zigzag-type GNR, a large overshooting current and slowly decaying transient charge are observed, which is due to the sharp lead spectra and the “even–odd” effect.