The three-qubit Toffoli gate is equivalent to the combination of two two-qubit controlled NOT gates and three two-qubit controlled phase-shift gates. The controlled NOT and phase-shift gates respectively comprise a combination of nuclear-magnetic-resonance pulse sequences and a free development operator of two nuclear spins with time. According to the order in which the controlled NOT and phase-shift gates act on the nuclear spin system, the nuclear-magnetic-resonance-based physical realization of a quantum Toffoli gate is achieved. The time-dependent Schr?dinger equation is numerically solved by the Suzuki formula to confirm the correctness and feasibility of the realization of the quantum Toffoli gate based on nuclear magnetic resonance.