The emergence of resistance to multiple antimicrobial agents in Gram-negative bacteria is a significant threat to public health, as it restricts the armamentarium of the clinician against these infections. The aim of this study was to determine the burden of extensively drug-resistant (XDR) and pandrug-resistant (PDR) Gram-negative bacteria at a tertiary-care centre. Antimicrobial susceptibility testing of 1240 clinical isolates of Gram-negative bacteria obtained from various clinical samples during the study period was carried out by the Kirby-Bauer disc diffusion method. Minimum inhibitory concentration of all antibiotics including tigecycline and colistin was determined by Vitek-2 automated susceptibility testing system. Out of 1240 isolates of Gram-negative bacteria, 112 isolates (9%) were resistant to all the antibiotics tested by Kirby-Bauer disc diffusion method. This finding was corroborated by Vitek-2. In addition, Vitek-2 found that 67 isolates were resistant to all antibiotics except tigecycline and colistin. A total of 30 isolates were susceptible to only colistin, and four isolates were susceptible to only tigecycline. It was also found that six isolates (excluding five isolates of Proteus spp.) were resistant to both colistin and tigecycline. Thus, 101 (8.1%) out of 1240 isolates were XDR and 11 isolates (0.9%) were PDR. The findings of this study reveal increased burden of XDR and PDR Gram-negative bacteria in our centre. It also highlights the widespread dissemination of these bacteria in the community. This situation warrants the regular surveillance of antimicrobial resistance of Gram-negative bacteria and implementation of an efficient infection control program.