In this paper, we investigate a (2+ 1)-dimensional Bogoyavlenskii-Kadontsev-Petviashili equation in a fluid, plasma or ferromagnetic thin film. Through the Bell polynomials, Hirota method and symbolic computation, the one-and two-kink-soliton solutions are derived. Backlund transformation, Lax pair and conservation laws are presented. Elastic collisions including the oblique, parallel, unidirectional and bidirectional collisions between the two-kink solitons are discussed. In addition, the relation between the velocities and wave numbers of the two-kink solitons are analysed. When wave numbers b(j) >0, upsilon(jx), the velocities in the x axis, increase with wave numbers a(j) increasing. With b(j) increasing, upsilon(jx) increase when a(j)(4) - 3b(2) j >0, while decrease when a(j)(4) - 3b(j)(2) < 0. upsilon(jy), the velocities in the y axis, increase with a(j) increasing and b(j) decreasing.