Using dynamic light scattering, we investigated supersaturated aqueous solutions of hen egg white lysozyme. We could observe the formation of aggregates only in solutions, from which crystals grew within a few days. The aggregates were grouped into smaller "units" and larger "clusters." The units consisted of a few molecules, whereas the clusters grew from about 100 nm to 1 mu m. At the beginning of aggregation, the number density of the units decreased, while that of the clusters increased. At this stage, unit-cluster aggregation proceeded. At the next stage, the number density of the units became constant, while that of the clusters began to decrease, which means that the units stopped aggregating and cluster-cluster aggregation started. The aggregation mechanism for the clusters fit well with the diffusion limited cluster aggregation model, but this model alone could not explain that the aggregates separated into two groups, corresponding to units and clusters, and that the units stopped aggregating during the aggregation process. We find that the observed aggregation process has several similarities to the liquid-liquid phase separation process, which occurs metastably in protein solution. Furthermore, using both models for diffusion limited aggregation and the liquid-liquid phase separation together, we could naturally explain the process of the cluster formation.