The aim of this paper was to study a generalised (2+1)-dimensional nonlinear Schrödinger equation, which can give us many important mathematical and physical models to illustrate various nonlinear phenomena in physical and engineering sciences. Based on a general Hirota bilinear form, the breather-type and non-singular rational solutions are presented. Akhmediev breather and Ma breather solutions can be considered as solutions representing the nonlinear propagation of the unstable model. In addition, by means of the bilinear transformation method, the fundamental rogue waves are given in terms of the Grammian determinant, which are shown to be line rouge waves. It is then demonstrated that the non-singular rational solutions generated via the long wave limit approach cover the rogue waves presented by the bilinear transformation method. The results presented in this paper exhibit the complexity and diversity of dynamical behaviour for the considered complex system.