In this paper, we have proposed some new upper bounds for the largest Z-eigenvalue of an irreducible weakly symmetric and nonnegative tensor, which improve the known upper bounds obtained in Chang et al. (Linear Algebra Appl 438:4166–4182, 2013), Song and Qi (SIAM J Matrix Anal Appl 34:1581–1595, 2013), He and Huang (Appl Math Lett 38:110–114, 2014), Li et al. (J Comput Anal Appl 483:182–199, 2015), He (J Comput Anal Appl 20:1290–1301, 2016).