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Let $H$ be the Hopf algebra $H_{c: \sigma_{0}}$ of Kashina [J. Algebra,232(2000),pp.617-663]. We give all simple Yetter-Drinfel'd modules $V$ over$H$, then classify all finite-dimensional Nichols algebras of $V$. The finitedimensional Nichols algebras of diagonal type are either $A_{1}, A_{2}$ orquantum planes, and non-diagonal type ones are $8$ or $16$ dimensional.

Finite dimensional Nichols algebras over $H_{c: \sigma_{0}}$ of Kashina