Based on the second-order moment of the power density, the beam width,far-field divergence angle and M² factor of nonparaxial truncated cosh-Gaussian （ChG） beams are studied. It is found that the M^2 factor of nonparaxial truncated ChG beams depends not only on the truncation parameter δ, decentered parameter α, but also on the initial waistwidth to wavelength ratio ωo/λ. M^2 may be less than one when d is small enough. As δ→0, the far-field divergence angle approaches an asymptotic value of θmax = 63.435°. For the special cases of α = 0（Ω0 = 0） and δ→∞ our results reduce to the M^2 of nonparaxial truncated Gaussian beams and nonparaxial untruncated ChG beams, respectively