The rotational spectrum of 3,3,3-trifluoropropene (CF3CH=CH2) in the ground and the first three excited states of the CF3 torsion has been analysed up to 75 GHz. Accurate rotational and centrifugal distortion constants have been determined. A-E splittings due to the internal rotation of the trifluoromethyl group have been observed in the second torsionally excited state using Fourier transform microwave spectroscopy. The torsional data have been analysed using the internal axis method (IAM) of Woods and the rho axis method (RAM). Both approaches lead to similar values of 612(2) cm-1 and 653·06(83)CM-1, respectively, for the IAM and RAM methods for the barrier height. An ab initio structure has been calculated and a near equilibrium structure has been determined using offsets derived empirically. Finally, an approximate equilibrium structure has been obtained by a combined use of the experimental moments of inertia and the ab initio results.