Spin transport characteristics of graphene have been extensively studied so far. The spin transport along the c-axis is however reported by rather limited number of papers. We have studied spin transport characteristics through graphene along the c-axis with permalloy(Py)/graphene(Gr)/Pt by gigahertz (GHz) and terahertz (THz) magnetization dynamics driven by femtosecond laser pulses. The relatively simple sample structure does not require electrodes on the sample. The graphene layer was prepared by chemical vapor deposition and transferred on Pt film. The quality of the graphene layer was characterized by Raman microscopy. Time-resolved magneto-optical Kerr effect is used to characterize gigahertz magnetization dynamics. Magnetization precession is clearly observed both for Pt/Py and Pt/Gr/Py. The Gilbert damping constant of Pt/Py was 0.015, indicating a spin pumping effect from Py to Pt. The Gilbert damping constant of Pt/Gr/Py was found to be 0.011, indicating that the graphene layer blocks spin injection. We also performed the measurement of THz emission for Pt/Py and Pt/Gr/Py. While a THz emission is clearly observed for Pt/Py, a substantial reduction of THz emission is observed for Pt/Gr/Py. With these two different experiments, and highly anisotropic resistivity of graphite, we conclude that the vertical spin transport is strongly suppressed by the graphene layer.