In this paper, we study the problem of inferring duplication history of a tandem gene family using the duplication model proposed by Tang et al.. We provide an efficient algorithm for inferring a duplication model for a given set of (gene) sequences by combining a linear-time algorithm, which is for determining whether a rooted tree is associated with a duplication model, with the nearest neighbor interchange operation. Finally, using our proposed method, we derive duplication hypotheses for an exon of a mucin gene MUC5B, a ZNF gene family, and a OR gene family.