Carbapenemase-producing Enterobacteriaceae (CPE) are one of the most detrimental species of antibiotic-resistant bacteria worldwide. Phage therapy has emerged as an effective strategy for the treatment of infections caused by CPE pathogens. In west Japan, the increasing occurrence of Klebsiella pneumoniae harboring the pKPI-6 plasmid, which encodes blaIMP-6, is a growing concern. To manage such major antimicrobial-resistant pathogens, we isolated 29 novel phages from sewage in Japan, targeting 31 strains of K. pneumoniae and one strain of Escherichia coli harboring the pKPI-6 plasmid. Electron microscopy analysis indicated that of the 29 isolated phages, 21 (72.4%), 5 (17.2%), and 3 (10.3%) belonged to Myoviridae, Siphoviridae, and Podoviridae, respectively. Host range analysis revealed that 20 Myoviridae members in isolated phages infected 25-26 strains of K. pneumoniae, indicating that most of the isolated phages have a broad host range. The K. pneumoniae Kp21 can only be infected by phage øKp_21, while Kp22 can be infected by more than 20 phages. We applied a phage cocktail, which consists of 10 phages, against Kp21 and Kp22 and found that the phage cocktail delayed the emergence of phage-resistant bacteria for Kp21 strain but not for the Kp22 strain. Furthermore, phage-resistant Kp21 (Kp21r) became prone to be infected from other bacteriophages as a "trade-off" of resistance to phage øKp_21. Our proposed phage set has an adequate number of phages to combat the K. pneumoniae strain isolated in Japan. Notably, our work demonstrates how a suitable phage cocktail diminishes the occurrence of phage-resistant bacteria.