This paper investigates the existence of infinitely many positive solutions for the second-order n-dimensional impulsive singular Neumann system \t\t\t−x″(t)+Mx(t)=λg(t)f(t,x(t)),t∈J,t≠tk,−Δx′|t=tk=μIk(tk,x(tk)),k=1,2,…,m,x′(0)=x′(1)=0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& -\\mathbf{x}^{\\prime\\prime}(t)+ M\\mathbf{x}(t)=\\lambda {\\mathbf{g}}(t)\\mathbf{f} \\bigl(t,\\mathbf{x}(t) \\bigr),\\quad t\\in J, t\\neq t_{k}, \\\\& -\\Delta {\\mathbf{x}}^{\\prime}|_{t=t_{k}}=\\mu {\\mathbf{I}}_{k} \\bigl(t_{k},\\mathbf{x}(t_{k}) \\bigr),\\quad k=1,2,\\ldots ,m, \\\\& \\mathbf{x}^{\\prime}(0)=\\mathbf{x}^{\\prime}(1)=0. \\end{aligned}$$ \\end{document} The vector-valued function x is defined by \t\t\tx=[x1,x2,…,xn]⊤,g(t)=diag[g1(t),…,gi(t),…,gn(t)],\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& \\mathbf{x}=[x_{1},x_{2},\\dots ,x_{n}]^{\\top }, \\qquad \\mathbf{g}(t)=\\operatorname{diag} \\bigl[g_{1}(t), \\ldots ,g_{i}(t), \\ldots , g_{n}(t) \\bigr], \\end{aligned}$$ \\end{document} where g_{i}in L^{p}[0,1] for some pgeq 1, i=1,2,ldots , n, and it has infinitely many singularities in [0,frac{1}{2}). Our methods employ the fixed point index theory and the inequality technique.