High-energy quark-quark scattering is calculated in quantum chromodynamics (QCD) using the infrared equation of Cornwall and Tiktopoulos. In contrast to ordinary quantum electrodynamics, the high-energy behavior is determined by the infrared structure. The infrared divergence is regulated by introduction of a small gluon mass; the amplitudes obtained agree with previous perturbation calculations (for t fixed, s-->∞) in QCD modified by the addition of a Higgs meson in the limit of small gluon mass. A proposal to calculate the infrared-finite behavior at fixed angle using asymptotic freedom is made, based on the hypothesis that the infrared divergence can be factored from an infrared-finite and renormalization-point-dependent part. The latter is calculable for the colorless exchange amplitude but not for the color exchange amplitude.