Memristor, which had been predicted a long time ago (Chua, L. O. IEEE Trans. Circuit Theory 1971, 18, 507), was recently invented (Strukov, D. B.; et al. Nature 2008, 453, 80). The introduction of a memristor is expected to open a new era for nonvolatile memory storage, neuromorphic computing, digital logic, and analog circuit. Furthermore, several breakthroughs were made for memristive phenomena and transistors with single-layer MoS2 (Sangwan, V. K.; et al. Nat. Nanotechnol. 2015, 10, 403. van der Zande, A. M.; et al. Nat. Mater. 2013, 12, 554. Liu, H.; et al. ACS Nano 2014, 8, 1031. Bessonov, A. A.; et al. Nat. Mater. 2015, 14, 199. Yuan, J.; et al. Nat. Nanotechnol. 2015, 10, 389). Herein, we demonstrate that 2H phase of bulk MoS2 possessed an ohmic feature, whereas 1T phase of exfoliated MoS2 nanosheets exhibited a unique memristive behavior due to voltage-dependent resistance change. Furthermore, an ideal odd-symmetric memristor with odd-symmetric I-V characteristics was successfully fabricated by the 1T phase MoS2 nanosheets via combining two asymmetric switches antiserially.