The high occurrence of nosocomial multidrug-resistant (MDR) microorganisms is considered a global health problem. Here, we report the draft genome sequence of a MDR Pseudomonas aeruginosa strain isolated in Brazil that belongs to the endemic clone ST277. The genome encodes important resistance determinant genes and consists of 6.7 Mb with a G+C content of 66.86% and 6,347 predicted coding regions including 60 RNAs.