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We introduce a class of rings which is a generalization of reflexive rings and $J$-reversible rings. Let $R$ be a ring with identity and $J\left(R\right)$ denote the Jacobson radical of $R$. A ring $R$ is called $J$-reflexive if for any $a,b\in R$, $aRb=0$ implies $bRa\subseteq J\left(R\right)$. We give some characterizations of a $J$-reflexive ring. We prove that some results of reflexive rings can be extended to $J$-reflexive rings for this general setting. We conclude some relations between $J$-reflexive rings and some related rings. We investigate some extensions of...