In order to solve the electrical performance limitations of horizontal multilayer graphene nanoribbon (H-MLGNR) based interconnect, a new geometric structure of vertical multilayer graphene nanoribbon (V-MLGNR) based interconnect is proposed in this paper. A numerical model for H-MLGNR and V-MLGNR based interconnects is established to investigate the performance in time and frequency domain, where the high-k dielectric materials (HKDM) are introduced for improving their transmission performance. The computation results demonstrate that the delay time for H-MLGNR and V-MLGNR based interconnects with embedded BaTiO3–Ni case can be reduced over 89.601 % and 93.723 % in comparison to the original H-MLGNR and V-MLGNR based interconnects, respectively. The corresponding 3-dB bandwidth for them can be expanded over 1.928 and 2.957 times, respectively. Moreover, it is manifested that the delay time of V-MLGNR based interconnect for the original, embedding the HfO2, TiO2, SrTiO3, BaTiO3, 6.0 vol% BaTiO3–Ni and 12.0 vol% BaTiO3–Ni cases can be reduced over 11.644 %, 13.269 %, 16.851 %, 22.311 %, 27.589 %, 33.608 % and 46.556 % as compared with the conventional H-MLGNR based interconnect, respectively. Meanwhile the corresponding 3-dB bandwidth of the former for the original, embedding the HfO2, TiO2, SrTiO3, BaTiO3, 6.0 vol% BaTiO3–Ni and 12.0 vol% BaTiO3–Ni cases can be enhanced over 1.113, 1.126, 1.155, 1.207, 1.266, 1.366 and 1.737 times as compared with the latter, respectively. In addition, the signal integrity of the proposed V-MLGNR based interconnects with embedded HKDM is greater than H-MLGNR based interconnects, while the power consumption of the former is slightly higher than the latter. Therefore, the proposed new interconnect structure concerning the V-MLGNR with embedded HKDM would be rewarding to enhance transmission performance of interconnect system in VLIS circuits.