Among these methods, the Hirota bilinear method is widely popular due to its simplicity and directness. Recently, rogue wave solutions [8,9] (being as a special solution of the rational solution) have drawn a big attention of mathematicians and physicists, which was first used to describe the momentous disastrous ocean waves. In contract to the rogue wave solution, lump solution is a special kind of rational solution, rationally localized in all directions in the space. In 2002, Lou et. al studied the lump solution with the variable separation method . Very recently, Ma et al. proposed the positive quadratic function to get the lump solution.Special examples of lump solutions have been found, such as the KPI equation , Boussinesq equation , BKP equation  and so on. As a kind of rational function solutions, lumps [14-16] are localized in all directions in the space, lump-type [17,18] solutions are localized in almost all directions in the space. Rogue waves [18,19] are localized in both space and time, and appear from nowhere and disappear without a trace , have taken the responsibility for numerous marine disasters. The (2+1)-dimensional ANNV Eq. (1) has been studied by many authors in recent years. for example, its algebraic-geometrical solutions have been explicitly given by using a nonlinearized method of Lax pair, the N-soliton solution and Pfaffian expression of solution have been discussed and derived by using the Hirota method  and some periodic wave solutions have been found in Ref. .