The dielectric properties of tetragonal hybrid perovskite CH3NH3PbI3 are studied through molecular dynamics at a temperature of 300 K in the presence of a finite electric field. The high-frequency dielectric constant ε∞ is found to be 4.5 along the a axis and 4.7 along the c axis. The values of the respective static dielectric constants ε0 are 43 ± 1 and 53 ± 3, much larger than the value of ∼25 pertaining to the orthorhombic phase, in which the organic cations cannot rotate. At frequencies below 3 cm–1, we observe a significant increase in ε0 by ∼23 (a axis) and ∼30 (c axis) compared to a vibrational approach, which does not account for the reorientation of the molecular units. The decomposition shows that the reorientation of the organic cations accounts for an increase of only ∼10. An increase of similar size results from the displacement of the cations within the cages of the lattice. The dominant contribution is found to arise from lattice vibrations coupled to the motion of the organic cations.