A molecular dynamics simulation of the shock-wave propagation in the face-centered cubic (FCC) structured C60 fullerene along the <100>, <110> and <111> crystallographic directions is performed. For this purpose, the response of the material under different shock-wave loadings is studied through Hugoniot curves. Three regimes of the material behavior have been observed from fully elastic to elastic-plastic to plastic. The Hugoniot elastic limit and the phase transition are also investigated along different crystallographic directions. It is shown that the shock wave travels faster along the <110> and <111> directions than in the <100> direction in the material. Comparing the results with the experimental data, it is found that the trends of the Hugoniot data are the same as the experiments. Also, the piston velocities corresponding to different structures, such as the FCC C60 fullerene, graphite like and final diamond like, are determined based on the Hugoniot results. Moreover, it is shown that after the phasetransition occurrence, at high piston velocities the material responses along the lowindex directions merge with each other; thus, an amorphous structure is expected for the final diamond-like phase.