  A common explanation for the CMB power asymmetry is to introduce a dipolar
modulation at the stage of inflation, where the primordial power spectrum is
spatially varying. If the universe in the stage of inflation is Finslerian, and
if the Finsler spacetime is non-reversible under parity flip, $x\rightarrow-x$,
then a three dimensional spectrum which is the function of wave vector and
direction is valid. In this paper, a three dimensional primordial power
spectrum with preferred direction is derived in the framework of Finsler
spacetime. It is found that the amplitude of dipolar modulation is related to
the Finslerian parameter, which in turn is a function of wave vector. The
angular correlation coefficients are presented, and the numerical results for
the anisotropic correlation coefficients over the multipole range $2<l<600$ are
given.
