Recently, the Planck 2013 results showed possible evidence for a dipolar power modulation of the CMB temperature fluctuations at low-l multipoles. This anomaly might imply certain deviations from statistical isotropy. To incorporate the Planck's data into the standard cosmological model, we propose an inflation model of the very early universe in an anisotropic spacetime. A generalized Friedmann-Robertson-Walker (FRW) metric is presented in the Randers-Finsler spacetime. We obtain the primordial power spectrum of the scalar perturbation with direction dependence, such as the dipolar modulation. This is consistent with the dipolar power modulation of the CMB anisotropy signaled by the Planck observation.