Electron collisional excitation strengths for transitions among the fine-structure levels of the ground 3s(2)3p(2) configuration and from the levels of 3s(2)3p(2) configuration to the levels of the excited 3s3p(3) and 3s(2)3p3d configurations in Fe XIII are calculated using a semirelativistic R-matrix approach. We considered 14 LS 3s(2)3p(2 3)P, D-1, S-1, 3s3p(3) D-3(0), P-3(0), D-1(0), S-3(0), P-1(0), 3s(2)3p3d P-3(0), D-1(0), D-3(0), F-3(0), F-1(0), and P-1(0) states of Fe XIII in the present calculation. The 14 LS states give rise to 26 fine-structure levels that are represented by configuration-interaction wave functions. The relativistic effects are included in the Breit-Pauli approximation via one-body mass correction, Darwin, and spin-orbit interaction terms in the scattering equations. Complicated resonance structures are explicitly included in the collision strengths. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range from 5 x 10(5) to 5 x 10(6) K.