In this paper, we focus on the integrability of a generalized (2+1)-dimensional equation with three arbitrary constants. By using Bell polynomials, the Hirota bilinear form is derived, as well as the N-soliton solutions are solved. Then the propagation and interaction of single and double soliton solutions have been simulated graphically, and the properties of solitary waves are well presented. By virtue of the Hirota bilinear form, the bilinear Bäcklund transformation with two arbitrary real functions is obtained. Based on this, we consider the Lax pair and infinite conservation laws of this equation.