Aggregation of native proteins in solution is of fundamental importance with regard to both the processing and the utilization of proteins. In the present work, a dynamic Monte Carlo simulation has been performed to give a molecular insight into the way in which native proteins aggregate in solution and to explore means of suppressing aggregation, using two proteins of different compositions and conformations represented by a two-dimensional (2D) lattice model (HP model). It is shown that the native HP protein with accessible hydrophobic beads on its surface is prone to aggregation. The aggregation of this protein is intensified when the solution conditions favor the partially unfolded conformation as opposed to either the native or fully unfolded conformations. In this case, the partially unfolded proteins form the cores of aggregates, which may also encapsulate the native protein. One way to inhibit protein aggregation is to introduce polymers of appropriate hydrophobicity and chain length into the solution, such that these polymer molecules wrap around the hydrophobic regions of both the unfolded and folded proteins, thereby segregating the protein molecules. Our simulation is consistent with experimental observations reported elsewhere and provides a molecular basis for the behavior of proteins in liquid environments.