Summary: Some characterization results of \(L_p\)-norm spherical distributions are obtained. It is proved that if \({\mathbf X}= (X_1,\dots, X_n)'\) has a \(L_p\)-norm spherical distribution having certain independence properties, then \(X_1, X_2,\dots, X_n\) must be i.i.d. with p.d.f. \(p(x)\propto e^{-|x|^p}/c\). Also, the largest characterization of \(L_p\)-norm spherical distributions is given.