We consider a generalization of a Ricci soliton as $\eta$-Ricci-Bourguignon solitons on a Riemannian manifold endowed with a semi-symmetric metric and semi-symmetric non-metric connection. We find some properties of $\eta$-Ricci-Bourguignon soliton on Riemannian manifolds equipped with a semi-symmetric metric and semi-symmetric non-metric connection when the potential vector field is torse-forming with respect to a semi-symmetric metric and semi-symmetric non-metric connection.