Summary: Generalized Lie superalgebra \(S(n)\) of Cartan-type is discussed. \(Z_2\)-graded of Lie superalgebra \(S(n)\) is generalized to \(Z_{2m}\)-graded, where \(m\) is an arbitrary positive integer. Simultaneously, restrictions on basic field \(F\) is relaxed to characteristic \(p\neq 2\). Since generalized Lie superalgebra \(S(n)=\oplus_{i\in Z}S(n)_i\) is \(Z\)-graded generalized Lie superalgebra, so is its derivation superalgebra \(\text{Der}(S)=\oplus_{t\in Z}\text{Der}_t(S)\). Hence, it is mainly studied that \(Z\)-graded components of derivation superalgebra of \(S(n)\). Furthermore, the derivation superalgebra of \(S(n)\) is determined.