Collision strengths and Maxwellian-averaged rate coefficients have been calculated for 3,160 non-vanishing transitions among 80 fine structure levels, dominated by configurations 3d^3^, 3d^2^4s, and 3d^2^4p in Fe VI. Collision strengths are calculated using the R-matrix method with a 34-term close-coupling target expansion and for electron energies up to 10 Rydbergs. Detailed comparisons of rate coefficients are presented with the relativistic Breit-Pauli calculations using a 19-level expansion corresponding to the first 8 LS terms dominated by the ground configuration 3d^3^. For the low-lying transitions of practical interest there is excellent agreement, better than 10%, among three sets of rate coefficients calculated using 34 term and 8-term non-relativistic calculations and the 19-level Breit-Pauli calculation, indicating that (i) the relativistic effects are not too significant, and (ii) the numerical uncertainties associated with the resolution of the extensive resonances in the collision strengths are small. Rate coefficients are tabulated in a range of temperatures, 10^4^-10^6^K, where Fe VI is normally abundant in radiatively photoionized or collisionally ionized plasmas sources. The present rates for Fe VI are expected to find applications in UV spectral diagnostics of hot stellar sources and planetary nebulae.