Molecular dynamics (MD) simulation of nanoindentation with a conical carbon indenter on graphite sheets and diamond is performed. The interactions of carbon indenter, graphite, and diamond atoms are described by the Tersoff–Brenner potential. Also, the Lennard–Jones potential function is employed to simulate the interactions between the indenter and the graphite and diamond atoms. The simulation results show that the maximum contact force increases with increasing conical angle due to an increase in the contact area. As the indentation velocity increases, the maximum contact force increases. However, the force decreases when the substrate temperature increases because of the weak interaction force between the atoms. Furthermore, the maximum contact force of nanoindentation with a conical indenter on the diamond was larger than that on the graphite sheets at the same indentation depth, velocity, and temperature.