Mechanically buckled components may exhibit negative stiffness, namely negative slopes of load-displacement curves. Negative-stiffness components are unstable under load control, but may be stabilized when embedded with positive-stiffness matrix in a form of composite. Negative-stiffness composites have been shown to exhibit stiffness greater than diamond, and their viscoelastic damping can be largely increased due to the negative-stiffness inclusions. Combining the negative-stiffness effects and nano-scale systems, we studied the mechanical system of a buckled carbon nanotube being compressed laterally with a carbon fullerene with molecular-dynamics (MD) simulations to explore its high effective stiffness. The buckled nanotube was laterally compressed with a C20 fullerene. The fullerenes are attached to the buckled nanotube via the carbon-carbon bonding with the Tersoff-Brenner interatomic potential. The force exerting on the fullerene and the corresponding displacement are monitored and recorded at each time step of 1 femtosecond. The constant particle number, volume and temperature (NVT) ensemble is chosen for the MD calculations. It is found the overall spring constant of the composite system under the loading condition is about 10 N/m in the initial loading state. Further loading on the system shows the overall stiffness is negative, indicating the interaction between the positive- and negative-stiffness was dominated by the nanotube. The calculated total load reveals that it is a low energy cost process to revert a buckled nanotube to an unbuckled state after creating a local buckling.