This paper proposed a new partial resonant 3.PHI. AC-DC boost converter of high efficiency using lossless snubber. The proposed converter, DCM (Discontinuous Current Mode) has a merit of simple controlled circuit because the input current control discontinuously. But turned off switching loss and stress of the switching device increase when the switch turned off at the peak of current. Therefore, the paper improves efficiency by adopting the PRS$^{2}$(Partial Resonant Soft Switching) in 3.PHI. AC-DC boost converter and makes the unity power factor. The PRS$^{2}$ is reduced a current/voltage stresses of switching devices. Also, a DCMPRS$^{2}$M(Discontinuous Conduction Mode Partial Resonant Soft Switching Method) appear the current and voltage equation of this circuit. The paepr examine in a 3.PHI. AC-DC boost converter and show the result of that.