Solvents have been widely used to enhance the solubility of carbon in the silicon melt. This effective approach can improve the efficiency of the top-seeded solution growth method for silicon carbide. This study proposes the use of rare earth elements (Pr, Ce, La) as solvent additives to enhance the growth efficiency of silicon carbide (SiC) crystals in the top-seeded solution growth (TSSG) method. A two-dimensional axisymmetric model was developed to analyze the thermal field, flow field, carbon solubility, carbon supersaturation distribution, and SiC growth rate in the Si-Ti-C, Si-Pr-C, Si-Ce-C, and Si-La-C melt systems. Key process parameters were optimized, such as the additive concentration, melt temperature distribution, crucible rotation speed, and seed crystal rotation speed. The maximum crystal growth rates in the Si-Ti-C, Si-Pr-C, Si-Ce-C, and Si-La-C systems were improved from 0.111, 0.249, 0.109, and 0.093 to 0.643, 5.171, 3.285 and 3.160 mm/h, respectively. Pr, Ce, and La additives were enhanced the effective SiC crystal growth rates by approximately 8, 5.1, and 4.9 times, compared with Ti as the solvent additive. The results reveal that Pr, Ce, and La as solubility enhancers can improve the efficiency of the top-seeded solution growth method for silicon carbide.