The authors generalize A. Stancu’s results [Adv. Appl. Math. 73, 43–58 (2016; Zbl 1331.52014)] on log-Minkowski inequality for non-symmetric convex bodies from volumes to quermassintegrals. The techniques are the same, including wording, as in [loc. cit.] exploiting the definition of quermassintegral measures.