Based on multi-stage triaxial experimental results of red sandstone with circumferential deformation control, the influence of confining pressure on strength and deformation behavior of red sandstone under multi-stage triaxial compression is investigated. The results show that the confining pressure has an obvious effect on the deformation parameters of red sandstone under multi-stage triaxial compression. A multi-stage triaxial compression experiment with only one specimen can be used to confirm the peak strength of rock under different confining pressures. Under single-stage and multi-stage triaxial compression, the peak strength behavior of red sandstone agrees better with the nonlinear Hoek–Brown criterion than the linear Mohr–Coulomb criterion. However, the difference between single-stage and multi-stage triaxial strength changes with different post-peak deformation values, and the reason for the difference, is discussed. To predict single-stage triaxial strength using the obtained multi-stage triaxial strength with only one specimen, a new method is put forward to revise multi-stage triaxial strength of red sandstone, which testifies to being reasonable. The concluding remarks are very useful and significant for deep geotechnical and underground structural engineering.