Particle collisions are considered within the context of f(R) gravity described by f(R)=R+2αR, where R stands for the Ricci scalar and α is a nonzero constant. The center of mass energy of head-on colliding particles moving in opposite radial directions near the naked singularity or horizon are considered. Collision of particles in the same direction near the event horizon yields finite energy while the energy of oppositely moving particles grows unbounded. Addition of a cosmological constant does not change this feature. Collision of a massless outgoing photon with an infalling particle and collision of two oppositely moving photons following null-geodesics are also taken into account.