The magnetorotational instability (MRI) is investigated using a two-fluid model. Electrons and singly charged ions are supposed to have the same angular velocity to eliminate the equilibrium current. The linear dispersion relation governing local MRI is derived. The instability criteria in the non-magnetized and weakly magnetized cases differ remarkably from those predicted by the one-fluid model. Based on the general magnetized case, we present the critical conditions for the occurrence of instability. Gyroeffects significantly alter the instability criterion and introduce four unstable regions, one of which is reduced to the magnetohydrodynamic result when the angular frequency is much less than the ion gyrofrequency. When the angular frequency is much less than the electron gyrofrequency, the ion gyroeffect contributes to the instability criterion and induces the Hall term.