Carbapenem-resistant Klebsiella pneumoniae (CRKP) has spread globally and emerged as an urgent public health threat. Bacteriophages are considered an effective weapon against multidrug-resistant pathogens. In this study, we report a novel lytic phage, kpssk3, which is able to lyse CRKP and degrade exopolysaccharide (EPS). The morphological characteristics of kpssk3 observed by transmission electron microscopy, including a polyhedral head and a short tail, indicate that it belongs to the family Podoviridae. A one-step growth curve revealed that kpssk3 has a latent period of 10 min and a burst size of 200 plaque-forming units (pfu) per cell. kpssk3 was able to lyse 25 out of 27 (92.59%) clinically isolated CRKP strains, and it also exhibited high stability to changes in temperature and pH. kpssk3 has a linear dsDNA genome of 40,539 bp with 52.80% G+C content and 42 putative open reading frames (ORFs). No antibiotic resistance genes, virulence factors, or integrases were identified in the genome. Based on bioinformatic analysis, the tail fiber protein of phage kpssk3 was speculated to possess depolymerase activity towards EPS. By comparative genomics and phylogenetic analysis, it was determined that kpssk3 is a new T7-like virus and belongs to the subfamily Autographivirinae. The characterization and genomic analysis of kpssk3 will promote our understanding of phage biology and diversity and provide a potential strategy for controlling CRKP infection.