A general expression for the electric field of a cylindrically polarized vector beam propagating in free space is derived on the basis of the exact fully vectorial solution of Maxwell equations in transverse Fourier space, which indicates that a cylindrical polarization can be regarded as the combination of radial and azimuthal polarizations, and the electric field retains cylindrical symmetry under the propagation. The simulation results denote that the longitudinal electric field depends on the ratio of the waist width to wavelength and the angle between the electrical vector and the radial direction; in particular, when this angle is 24.5°, a flattop intensity distribution is obtained at the plane z=0.