  We introduce the notion of Johnson pseudo-Connes amenability for dual Banach
algebras. We study the relation between this new notion with the various
notions of Connes amenability like Connes amenability, approximate Connes
amenability and pseudo Connes amenability. We also investigate some hereditary
properties of this new notion. We prove that for a locally compact group $G$,
$M(G)$ is Johnson pseudo-Connes amenable if and only if $G$ is amenable. Also
we show that for every non-empty set $I$, $\mathbb{M}_I(\mathbb{C})$ under this
new notion is forced to have a finite index. Finally, we provide some examples
of certain dual Banach algebras and we study their Johnson pseudo-Connes
amenability.
