Alloy nanoclusters have received extensive attention because they can achieve bifunctional properties by making good use of the cooperative effect of two metals. In this paper, an improved Basin-Hopping Monte Carlo (BHMC) algorithm is proposed to investigate the structural stabilities of Fe-Pt alloy nanoclusters. Different cluster sizes and chemical compositions are considered. Moreover, a similarity function is introduced to analyze the structural similarity between the stable structures of alloy clusters and those of their monometallic clusters. Meanwhile, the atomic distributions of Fe-Pt alloy clusters are considered for their stable structures. The results indicate that for Fe-Pt alloy clusters with the size N 24, there is no significant structural evolution with the increase of cluster size. Fe atoms prefer to segregate at the peripheral positions of the clusters, while Pt atoms tend to occupy the interior. The same distribution result can be obtained for the structures of clusters with different compositions. With Fe composition increasing, this distribution trend is more pronounced for the Fe-Pt alloy clusters. In addition, by calculating the structural similarity function between alloy and monometallic clusters, we find that the stable structures of Fe-Pt alloy clusters gradually vary with composition ratio. Moreover, when the Fe atoms or Pt atoms are added into the Fe-Pt alloy system, they change the stable structures of Fe-Pt alloy clusters, resulting in a different structure from Fe and Pt monometallic ones. Also, the structural similarity is different when the Fe composition varies. Furthermore, the best stable structures of Fe-Pt clusters with different compositions and sizes are obtained by calculating the second-order finite difference in energy of Fe-Pt alloy clusters.