We measure the two-dimensional electronic spectra of the LHCII(M)-CP29-CP24 complex in photosystem II (PSII) and provide the first study of the ultrafast excitation energy transfer (EET) processes of an asymmetric and native light-harvesting assembly of the antenna of PSII. With comparisons to LHCII, we observe faster energy equilibrations in the intermediate levels of the LHCII(M)-CP29-CP24 complex at 662 and 670 nm. Notably, the putative "bottleneck" states in LHCII exhibit faster effective dynamics in the LHCII(M)-CP24-CP29 complex, with the average lifetime shortening from 2.5 ps in LHCII to 1.2 ps in the bigger assembly. The observations are supported by high-level structure-based calculations, and the accelerated dynamics can be attributed to the structural change of LHCII(M) in the bigger complex. This study shows that the biological functioning structures of the complexes are important to understand the overall EET dynamics of the PSII supercomplex.