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Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A_{1}, A_{2},\ldots, A_{k}$\end{document}A1,A2,…,Ak be nonnegative matrices. In this paper, some upper bounds for the spectral radius \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho(A_{1}\circ A_{2}\circ\cdots\circ A_{k})$\end{document}ρ(A1∘A2∘⋯∘Ak) are proposed. These bounds generalize some existing results, and comparisons between these bounds are also considered.