Acinetobacter baumannii is a non-fermenting, gram-negative bacterium. In recent years, the frequency of A. baumannii infections has continued to increase, and multidrug-resistant strains are emerging in hospitalized patients. Therefore, as therapeutic options become limited, the potential of phages as natural antimicrobial agents to control infections is worth reconsidering. In our previous study, we isolated ten virulent double-stranded DNA A. baumannii phages, ϕAB1–9 and ϕAB11, and found that each has a narrow host range. Many reports indicate that receptor-binding protein of phage mediates host recognition; however, understanding of the specific interactions between A. baumannii and phages remains very limited. In this study, host determinants of A. baumannii phages were investigated. Sequence comparison of ϕAB6 and ϕAB1 revealed high degrees of conservation among their genes except the tail fiber protein (ORF41 in ϕAB1 and ORF40 in ϕAB6). Furthermore, we found that ORF40ϕAB6 has polysaccharide depolymerase activity capable of hydrolyzing the A. baumannii exopolysaccharide and is a component of the phage tail apparatus determining host specificity. Thus, the lytic phages and their associated depolymerase not only have potential as alternative therapeutic agents for treating A. baumannii infections but also provide useful and highly specific tools for studying host strain exopolysaccharides and producing glycoconjugate vaccines.