Based on the methods of vector angular spectrum of electromagnetic beams and stationary phase, the analytical expressions of TE and TM terms and energy flux distributions of cosh-Gaussian (ChG) vortex beams in the far field are derived, and used to study the phase singularities and energy flux distributions of the ChG vortex beams. It is shown that the density and position of optical vortices will vary by changing decentered parameter or waist width in the ChG vortex beams. The vortex off-axis distance leads to an asymmetric spatial distribution of energy flux. With gradually increasing vortex off-axis distance, dark spots around the origin will move toward the origin center.