In the present paper, we focus on the representation theory of the 8m-dimensional non-pointed bialgebra \({\mathcal {B}_{8m}}\) , which is obtained from Ore extensions of the Sweedler’s Hopf algebra. We get a basis of \({\mathcal {B}_{8m}}\) by some \({\mathcal {B}_{8m}}\) -modules at first, then by the primitive orthogonal idempotents, we draw the quiver of \({\mathcal {B}_{8m}}\) . After constructing all the mutually non-isomorphic indecomposable \({\mathcal {B}_{8m}}\) -modules, we provide the decomposition formulas for the tensor products between all indecomposable modules. At last, we describe the representation ring of \({\mathcal {B}_{8m}}\) by generators and relations clearly.
