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Let $(1\to N_n\to G_n\to Q_n \to 1)_{n\in \mathbb{N}}$ be a sequence ofextensions of countable discrete groups. Endow $(G_n)_{n\in \mathbb{N}}$ withmetrics associated to proper length functions on $(G_n)_{n\in \mathbb{N}}$respectively such that the sequence of metric spaces $(G_n)_{n\in \mathbb{N}}$have uniform bounded geometry. We show that if $(N_n)_{n\in \mathbb{N}}$ and$(Q_n)_{n\in \mathbb{N}}$ are coarsely embeddable into Hilbert space, then thecoarse Novikov conjecture holds for the sequence $(G_n)_{n\in \mathbb{N}}$,which may not admit a coarse embedding into Hilbert space.

The coarse Novikov conjecture for extensions of coarsely embeddable groups