A molecular dynamics simulation study has been performed for a large-sized system consisting of 106 liquid metal Al atoms to investigate the formation and magic number characteristics of various clusters formed during solidification processes. The cluster-type index method (CTIM) is adopted to describe various types of cluster by basic clusters. It is demonstrated that the icosahedral cluster (120120) is the most important basic cluster, and that it plays a critical role in the microstructure transition. A new statistical method has been proposed to classify the clusters as some group levels according to the numbers of basic clusters contained in each cluster. The magic numbers can be determined by the respective peak value positions of different group levels of clusters, and the magic number sequence in the system is 13, 19, 25(27), 31(33), 38(40), 42(45), 48(51), 55(59), 61(65), 67,... the numbers in the brackets are the second magic number of the corresponding group levels of clusters. This magic number sequence is in good agreement with the experimental results obtained by Schriver and Harris et al, and the experimental results can be reasonably well explained.