Pseudomonas aeruginosa, a major cause of nosocomial infections, has been categorized by World Health Organization as a critical pathogen urgently in need of effective therapies. Bacteriophages or phages, which are viruses that specifically kill bacteria, have been considered as alternative agents for the treatment of bacterial infections. Here, we discovered a lytic phage targeting P. aeruginosa, designated as JJ01, which was classified as a member of the Myoviridae family due to the presence of an icosahedral capsid and a contractile tail under TEM. Phage JJ01 requires at least 10 min for 90% of its particles to be adsorbed to the host cells and has a latent period of 30 min inside the host cell for its replication. JJ01 has a relatively large burst size, which releases approximately 109 particles/cell at the end of its lytic life cycle. The phage can withstand a wide range of pH values (3–10) and temperatures (4–60°C). Genome analysis showed that JJ01 possesses a complete genome of 66,346 base pairs with 55.7% of GC content, phylogenetically belonging to the genus Pbunavirus. Genome annotation further revealed that the genome encodes 92 open reading frames (ORFs) with 38 functionally predictable genes, and it contains neither tRNA nor toxin genes, such as drug-resistant or lysogenic-associated genes. Phage JJ01 is highly effective in suppressing bacterial cell growth for 12 h and eradicating biofilms established by the bacteria. Even though JJ01-resistant bacteria have emerged, the ability of phage resistance comes with the expense of the bacterial fitness cost. Some resistant strains were found to produce less biofilm and grow slower than the wild-type strain. Among the resistant isolates, the resistant strain W10 which notably loses its physiological fitness becomes eight times more susceptible to colistin and has its cell membrane compromised, compared to the wild type. Altogether, our data revealed the potential of phage JJ01 as a candidate for phage therapy against P. aeruginosa and further supports that even though the use of phages would subsequently lead to the emergence of phage-resistant bacteria, an evolutionary trade-off would make them more sensitive to antibiotics.