In this paper, an equivalence (called Schur-Weyl duality) of module categories between the trigonometric (resp., rational) Cherednik algebra associated to the symmetric group \(S_l\) and a (resp., subalgebra \(\mathbb{L}\) of a) Yangian \(LY\) for the loop algebra \(Lsl_n\) is proved, which generalizes similar Schur-Weyl dualities between the symmetric group \(S_l\) and the Lie algebra \(sl_n\) for \(n\geq l+1\), between degenerate affine Hecke algebras and Yangians, and between double affine Hecke algebras and toroidal quantum algebras.