The layered compound SrFeO2 with an Feat square-planar motif exhibits an unprecedented pressure-induced spin state transition (S = 2 to 1), together with an insulator-to-metal (1-M) and an antiferromagnetic-to-ferromagnetic (AFM-FM) transition. In this work, we have studied the pressure effect on the structural, magnetic, and transport properties of the structurally related two-legged spin ladder Sr3Fe2O5. When pressure was applied, this material first exhibited a structural transition from Immm to Ammm at P-s = 30 +/- 2 GPa. This transition involves a phase shift of the ladder blocks from (1/2,1/2,1/2) to (0,1/2,1/2), by which a rock-salt type SrO block with a 7-fold coordination around Sr changes into a CsCl-type block with 8-fold coordination, allowing a significant reduction of volume. However, the S = 2 antiferromagnetic state stays the same. Next, a spin state transition from S = 2 to S = 1, along with an AFM-FM transition, was observed at P-c = 34 +/- 2 GPa, similar to that of SrFeO2. A sign of an I-M transition was also observed at pressure around P-c. These results suggest a generality of the spin state transition in square planar coordinated S = 2 irons of n-legged ladder series Srn+1FenO2n+1 (n = 1, 2, 3, ... ). It appears that the structural transition independently occurs without respect to other transitions. The necessary conditions for a structural transition of this type and possible candidate materials are discussed.