Ab initio Hartree-Fock and density functional theory calculations using the 6-31G* basis set were carried out to study the molecular structure and vibrational spectrum of fluorene (FR). Two density functionals were employed : the (1) Becke-Lee-Yang-Parr (BLYP) functional and (2) the Becke 3-Lee-Yang-Parr (B3LYP) functional. Comparison of the calculated and experimental vibrational spectra reveals that the B3LYP calculations are quite accurate in predicting the vibrational frequencies and modes. We report the results of new assignments of the fundamental vibrational frequencies obtained on the basis of the calculations. The new assignments show a one-to-one correspondence between the observed and calculated fundamentals.