Summary: In this work, we are concerned with a problem of a logarithmic nonlinear wave equation with time-varying delay term. We established the local existence result and we proved a blow up result for the solution with negative initial energy under suitable conditions. This improves earlier results in the literature for time-varying delay M. Kafini and S. Messaoudi [Appl. Anal. 99, No. 3, 530–547 (2020; Zbl 1439.35090)].