Under consideration in this paper is a Volterra lattice system. Through symbolic computation, the Lax pair and conservation laws are derived, an integrable lattice hierarchy and an N-fold Darboux transformation (DT) are constructed for this system. Furthermore, N-soliton solutions in terms of determinant are generated with the resulting N-fold DT. Structures of the one-, two-and three-soliton solutions are shown graphically. Overtaking inelastic solitonic interactions between/among the two and three solitons are discussed by figures plotted.