The model of cluster growth by diffusion-limited aggregation of clusters is studied in two dimensions and the cluster size distribution n s (t) is determined as a function of the cluster size s and the time t. A dynamic scaling function of the form n s (t)∼ t− w s− τ f (s t z) is proposed and is shown to lead to the scaling relation w=(2− τ) z among the critical exponents. The simulation results support this scaling law.