Abstract: Based on the Rayleigh-Sommerfeld diffraction integrals, the closed-form expression of truncated nonparaxial cosh-Gaussian (ChG) beams in free space is derived, and some special cases are discussed. The power in the bucket (PIB) of nonparaxial regime is introduced to characterize the beam quality of truncated nonparaxial beams in the far field. It is found that the intensity and the PIB of truncated nonparaxial ChG beams depend on the waist-width-to-wavelength ratio, decentered parameter, truncation parameter and the PIB additionally depends on the bucket size. For a given bucket size, the larger waist-width-to-wavelength ratio, truncation parameter and smaller decentered parameter result in the better power focus ability in the far field and the better beam quality.