The current study aimed to determine the molecular mechanisms of carbapenem and colistin resistance among the clinical isolates of Klebsiella pneumoniae from hospitalized patients admitted to a university hospital in Eastern Algeria. In total, 124 non-duplicate isolates of K. pneumoniae were collected from September 2018 to April 2019. Bacterial identification was performed using MALDI-TOF MS. The presence of extended spectrum β-lactamase (ESBL) genes, carbapenemase genes, chromosomal mutation and mcr genes in colistin-resistant K. pneumoniae were evaluated by PCR. ESBLs represented a rate of 49.1% and harbored blaCTX-M, blaTEM and blaSHV genes. Concerning carbapenems, 12 strains (9.6%) were resistant to ertapenem (MIC: 1–32 μg/mL), of which one strain (0.8%) was also resistant to imipenem (MIC: 32 μg/mL). Among these strains, nine (75%) harbored blaOXA-48 gene. Seven strains (5.6%) expressed resistance to colistin (MIC: 2–32 μg/mL), of which two harbored mcr-8 and mgrB genes simultaneously. The existence of a double resistance to colistin in the same strain is new in Algeria, and this could raise concerns about the increase in levels of resistance to this antibiotic (MIC: 32 μg/mL). The mgrB gene alone was observed in five isolates (71.4%), including two strains harboring blaOXA-48. This is the first report revealing the presence of K. pneumoniae strains carrying the blaOXA-48 gene as well as a mutation in the mgrB gene. Large-scale surveillance and effective infection control measures are also urgently needed to prevent the outbreak of various carbapenem- and colistin-resistant isolates.