Taking the Laguerre-Gaussian (L-G) beam for example, the changes in the degree of paraxiality for monochromatic beams are studied in detail. It is shown that the beam parameters, including mode indiex, relative waist width, propagation through a paraxial ABCD optical system, and diffraction by an aperture may change the degree of paraxiality. But the degree of paraxiality remains unchanged in free-space propagation. The results are illustrated by numerical examples and interpreted in physics by relating the degree of beam paraxiality with the far-field divergence angle.