  The $N$-jettiness subtraction has proven to be an efficient method to perform
differential QCD next-to-next-to-leading order (NNLO) calculations in the last
few years. One important ingredient of this method is the NNLO soft function.
We calculate this soft function for one massive colored particle production at
hadron colliders. We select the color octet and color triplet cases to present
the final results. We also discuss its application in NLO and NNLO differential
calculations.
