The supersymmetry algebra of Wess and Zumino has been generalized to incorporate explicitly the baryon-number operator. Constraints on the algebraic structure due to the finite dimensionality of its representations have been determined. In the rest frame where the supersymmetry generator has only two components, it is shown that an irreducible representation cannot have more than three adjacent baryon numbers. The octet representations in the (B, J3) space for various SU(3) states are shown to accommodate most of the prominent hadrons. The product representation of two octets has been reduced to an irreducible octet component, and the consequences on the coupling constants have been determined. The implication on the couplings among the physical hadrons is discussed.