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Let G be a simple connected graph with n vertices and m edges,LG be the line graph of G and λ1(LG)≥λ2(LG)≥...≥λm(LG) be the eigenvalues of the graph LG.In this paper,the range of eigenvalues of a line graph is considered.Some sharp upper bounds and sharp lower bounds of the eigenvalues of LG are obtained.In particular,it is proved that -2cos((π)/(n))≤λn-1(LG)≤n-4 and λn(LG)=-2 if and only if G is bipartite.