In this paper, a (2 + 1)-dimensional nonlinear Schrodinger equation for a (2 + 1)-dimensional Heisenberg ferromagnetic spin chain with the bilinear and anisotropic interactions is investigated. Via the Hirota method and symbolic computation, bilinear forms and multi-soliton solutions are derived. The one, two and three solitons are analyzed graphically and we find the amplitudes and widths of the two and three solitons keep invariant after each interaction. The bell-shape one soliton as well as parallel, crossed two and three solitons are respectively observed. Through the asymptotic analysis, expressions which denote the two solitons before and after the interactions are obtained and interactions between the two solitons are proved to be elastic. (C) 2016 Elsevier Ltd. All rights reserved.