In this paper, a simple technique to determine the geometrical properties of fractional Fourier transform of paraxial beams based on the phase space beam transformation matrix is presented. Taking the elliptic Gaussian beam as an example, we have compared our analysis technique with that of previous work and found that the present method is more reliable in predicting the geometrical properties of fractional Fourier transform of beams and has the advantage of clear intuitive physical insight into beam propagation and transformation process from a geometrical viewpoint. This technique provides a simple and convenient way to study propagation and transformation properties of light beams in a novel approach.