[en] An integrable lattice hierarchy is constructed from a discrete matrix spectral problem, in which one of the Suris systems is the first member of this hierarchy. Some related properties such as Hamiltonian structure of this lattice hierarchy are discussed. The Suris system is solved by the N-fold Darboux transformation. As a result, the multi-soliton solutions are derived and the soliton structures along with the interaction behaviors among solitons are shown graphically. Finally, the infinitely many conservation laws of the Suris system are given.