In this paper, I introduce a new generalization of essential submodules, namely $\delta$-essential submodules. A submodule $A$ of an $R$-module $M$ is called $\delta$-essential in $M$ provided that for every nonzero $\delta$-small submodule $B$ of $M$ has a nonzero intersection with $A$. Appling this concept, I define a generalization of extending module entitled $\delta$-extending moduels and investigate their some general properties.