This paper consists of two parts. In the first part, we prove that when \({\mathfrak {g}}\) is a simple basic Lie superalgebra with a principal odd nilpotent element f, the W-algebra \(W^k({\mathfrak {g}}, F)\) for \(F=-\frac{1}{2}{[}f,f{]}\) is isomorphic to the SUSY W-algebra \(W^k(\bar{{\mathfrak {g}}},f)\) via screening operators, which implies the supersymmetry of \(W^k({\mathfrak {g}}, F)\) . In the second part, we show that a finite SUSY W-algebra, which is a Hamiltonian reduction of \(U(\widetilde{{\mathfrak {g}}})\) for the SUSY Takiff algebra \(\widetilde{{\mathfrak {g}}}={\mathfrak {g}}\otimes \wedge (\theta )\) is isomorphic to the Zhu algebra of a SUSY W-algebra. As a corollary, we show that a finite SUSY principal W-algebra is isomorphic to a finite principal W-algebra.
