There is a pressing need for new therapeutics to combat multidrug- and carbapenem-resistant bacterial pathogens. This challenge prompted us to use a long short-term memory (LSTM) language model to understand the underlying grammar, i.e. the arrangement and frequencies of amino acid residues, in known antimicrobial peptide sequences. According to the output of our LSTM network, we synthesized 10 peptides and tested them against known bacterial pathogens. All of these peptides displayed broad-spectrum antimicrobial activity, validating our LSTM-based peptide design approach. Our two most effective antimicrobial peptides displayed activity against multidrug-resistant clinical isolates of Escherichia coli, Acinetobacter baumannii, Klebsiella pneumoniae, Pseudomonas aeruginosa, Staphylococcus aureus, and coagulase-negative staphylococci strains. High activity against extended-spectrum β-lactamase, methicillin-resistant S. aureus, and carbapenem-resistant strains was also observed. Our peptides selectively interacted with and disrupted bacterial cell membranes and caused secondary gene-regulatory effects. Initial structural characterization revealed that our most effective peptide appeared to be well folded. We conclude that our LSTM-based peptide design approach appears to have correctly deciphered the underlying grammar of antimicrobial peptide sequences, as demonstrated by the experimentally observed efficacy of our designed peptides.