Nitrogen-vacancy centers in diamond are ideal platforms for quantum simulation, which allows one to handle problems that are intractable theoretically or experimentally. Here we propose a digital quantum simulation scheme to simulate the quantum phase transition occurring in an ultrathin topological insulator film placed in a parallel magnetic field [Zyuzin et al., Phys. Rev. B 83, 245428 (2011)PRBMDO1098-012110.1103/PhysRevB.83.245428]. The quantum simulator employs high quality spin qubits achievable in nitrogen-vacancy centers. With a series of precise controls, the dynamics of the spin system is made capable of simulating the dynamics of the simulated TI system. The eigenenergies of the TI system are extracted by a quantum algorithm of finding eigenvalues. The scheme can be realized with existing technologies. An operation time of the order of 100 s is estimated for each individual run.