. In this work, the investigation of spacetimes admitting semiconformal curvature tensor in f(R)-gravity theory is the major goal. First, semiconformally flat spacetimes in the presence of f(R)-gravity are investigated, and the relationship between isotropic pressure and energy density is discovered. Some energy conditions are then taken into account. Finally, spacetimes with divergence-free semiconformal curvature tensors in f(R)- gravity are explored.