On the basis of the second-order moment of the power density, beam width, far-field divergence angle and M2 factor nonparaxial cosine-squared Gaussian beams were illustrated and analyzed with numerical simulation. The conclusions are as following. 1) The waist width W0(0) increases with increasing w0/λ parameter. W0(0) decreases with increasing decentred parameter α when w0/λ is relatively large (w0/λ≥0.5). 2) As the parameter w0/λ→0, the far-field divergence angle approaches an asymptotic value of θ0max=63.435°, which is independent of the decentred parameter α. 3) In the nonparaxial regime, the M2 factor of cosine-squared Gaussian beams depends not only on the decentred parameter α, but also on the initial waist-width to wavelength ratio w0/λ, the M2 factor may be less than 1 as w0/λ becomes small enough. The M2 factor does not always vary monotonically with w0/λ for different decentred parameter α, and it increases with increasing w0/λ and reaches the maximum value, then gradually decreases, and finally tends to be a saturated value.