Using a cluster model based on the Woods-Saxon potential, alpha-particle decays from excited states in Mg-24 have been systematically investigated. Calculations can in general reproduce experimental data, noticing the fact that the preformation factor P of alpha particle in alpha-decaying nuclei is of order from 10(0) to 10(-2). This can be the evidence for the alpha+Ne-20 structure in Mg-24. Meanwhile, the results also show the existence of other configurations, such as O-16+2 alpha. Since the calculated decay widths are very sensitive to the angular momentum carried by the outgoing cluster (alpha particle), our results could serve as a guide to experimental spin assignments.