We performed an unbiased search for low-energy structures of medium-sized neutral Si-n and Ge-n clusters (n = 25-33) using a genetic algorithm (GA) coupled with tight-binding interatomic potentials. Structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Si-n and Ge-n clusters of n = 25-29 compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Si-n and Ge-n (n = 29-33) and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Si-n (n = 25-33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE-calculated results. In the size range of 25-33, the corresponding Ge-n clusters hold the prolate growth pattern. The relative stabilities and different structural motifs of Si-n and Ge-n (n = 25-33) clusters were studied, and the changes of small cluster structures, when acting as building blocks of large clusters, were also discussed.