The Free Core Nutation (FCN) is a rotational mode related to non-alignment of the rotation axis of the core and of the mantle. There is a big gap between the observed FCN period (about 430 Sidereal days) and the theoretically calculated period (ranging from 450 Sd to 470 Sd). We propose a spectral element method to compute the period of FCN and obtain a good result, which is $437$ Sd. {\bf Keywords: } FCN, Spectral Element Method