A new method to measure the top-quark mass in high energetic hadron collisions is presented. We use theoretical predictions calculated at next-to-leading order accuracy in quantum chromodynamics to study the ( normalized) differential distribution of the t (t) over bar + 1-jet cross section with respect to its invariant mass root s(t (t) over barj). The sensitivity of the method to the top-quark mass together with the impact of various theoretical and experimental uncertainties has been investigated and quantified. The new method allows for a complementary measurement of the top-quark mass parameter and has a high potential to become competitive in precision with respect to established approaches. Furthermore we emphasize that in the proposed method the mass parameter is uniquely defined through one-loop renormalization.