The focus of this article is to tackle the challenging task of unresolved-group object (UO) tracking by exploiting the Poisson multi-Bernoulli mixture (PMBM) filter, named UO-PMBM. Specifically, according to the UO likelihood function, the probability generating functional tool and functional derivative are first used to derive the filtering recursion expressions of the UO-PMBM. Then, detailed descriptions of the Gaussian mixture (GM) implementations are described. Lastly, the effectiveness of the proposed UO-PMBM approach is demonstrated through simulation experiments.