In this paper, we investigate the long-time behavior and solvability of the reaction-diffusion equation, which has a polynomial growth nonlinearity of arbitrary order, with Robin boundary condition. We begin this paper with the existence and uniqueness of the solution to the problem. For the long-time behavior, we firstly prove the existence of an absorbing set in two different spaces. Secondly, for the autonomous case, the existence of a global attractor is obtained in W-2(1) (Omega) boolean AND L rho+2 (Omega). (C) 2014 Elsevier Ltd. All rights reserved.