The main purpose of this work is solving a generalized (2 + 1)-dimensional nonlinear wave equation via ∂¯∂¯∂¯∂¯∂¯-dressing method. The key to this process is to establish connection between characteristic functions and ∂¯∂¯∂¯∂¯∂¯-problem. With use of Fourier transformation and Fourier inverse transformation, we obtain explicit expressions of Green’s function and give two characteristic functions corresponding to general potential. Further, the ∂¯∂¯∂¯∂¯∂¯-problem is constructed by calculating ∂¯∂¯∂¯∂¯∂¯ derivative of characteristic function. The solution of ∂¯∂¯∂¯∂¯∂¯-problem can be shown by Cauchy–Green formula, and after determining time evolution of scatter data, we can give solutions of the (2 + 1)-dimensional equation.