Liquid-crystallization-driven self-assembly (LCDSA) is an emerging methodology, which has been employed to construct controllable 1D nanostructures. However, 2D nanostructures via living LCDSA are rarely reported, and the complicated growth kinetics are not well-known. Herein, we perform Brownian dynamics (BD) simulations to investigate the 2D living growth of disklike micelles via LCDSA of rod-coil block copolymers. The 2D seeded-growth behavior is achieved by incorporating the unimers onto the edges of disklike seeds with smectic-like liquid-crystalline (LC) cores. The fluidity of such LC-like micellar cores is conducive to the chain adjustments of rod blocks during the 2D living growth process. The apparent growth rate and unique self-similarity kinetics are governed by the interplay between the variations in the growth rate coefficient and the reactive sites at the micelle edges. This work provides an in-depth understanding of the 2D living growth of micelles and guidance to construct well-defined 2D hierarchical nanostructures.