Collision strengths for transitions between the 3s(2)3p(4) P-3(2,1,0), D-1(2), and S-1(0) levels and from these levels to the 3s3p(5) (3)p(2,1,0,)degrees and (1)P(1)degrees levels of Fe XI are calculated using a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS 3s(2)3p(4) P-3, D-1, S-1, 3s3p(5) P-3 degrees, P-1 degrees, 3s(2)3p3(S-4 degrees)3d D-3 degrees, 3s(2)3p(3)((2)p degrees)3d P-1,P-3 degrees D-1,D-3 degrees, F-1,F-3 degrees, 3S(2)3p(3)(D-2 degrees)3d S-1,S-3 degrees, (1,3)p degrees, D-1,D-3 degrees, F-1,F-3 degrees states are included in our calculation. These target levels are represented by configuration-interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Complicated resonance structures are found to enhance the collision strengths significantly for many transitions in the threshold energy regions. Our collision strengths are compared with the available results of Bhatia & Doschek at 8.0, 16.0,and 24.0 ryd. The collision strengths are integrated over a Maxwellian distribution of electron energies to give effective collision strengths over a wide temperature range.