Gelation through the liquid-liquid contact between a polymer solution and a gelator solution has been attempted with various combinations of gelator and polymer solutions. In many combinations, the gel growth dynamics is expressed asX∼t, whereXis the gel thickness andtis the elapsed time, and the scaling law holds for the relationship betweenXandt. In the blood plasma gelation, however, the crossover of the growth behavior fromX∼tin the early stage toX∼tin the late stage was observed. It was found that the crossover behavior is caused by a change in the rate-limiting process of growth from the free-energy-limited process to the diffusion-limited process. How, then, would the crossover phenomenon be described in terms of the scaling law? We found that the scaling law does not hold in the early stage owing to the characteristic length attributable to the free energy difference between the sol-gel phases, but it does in the late stage. We also discussed the analysis method for the crossover in terms of the scaling law.