Treatment of infections caused by Acinetobacter spp., particularly A. baumannii, is a major clinical problem due to its high rates of antibiotic resistance. New strategies must be developed; therefore, restoration of β-lactam efficacy through the use of β-lactamase inhibitors is paramount. Activities of the antibiotics imipenem, meropenem, cefepime, and sulbactam in combination with the penicillin-sulfone inhibitor LN-1-255 were tested by microdilution against 148 isolates of Acinetobacter spp. collected in 14 hospitals in Spain in 2020. Relevantly, the MIC90 (i.e., minimum concentration at which 90% of isolates were inhibited) of antibiotics in combination with LN-1-255 decreased 4- to 8-fold for all of the Acinetobacter isolates. Considering only the carbapenem-resistant A. baumannii isolates, which produce carbapenem-hydrolyzing class D β-lactamases, the addition of LN-1-255 decreased the resistance rates from 95.1% to 0% for imipenem, from 100% to 9.8% for meropenem, from 70.7% to 7.3% for cefepime, and sulbactam resistance rates from 9.8% to 0% and intermediate susceptibility rates from 53.7% to 2.4%. The inhibitor also decreased the minimum inhibitory concentrations (MICs) when tested against non-carbapenem-resistant Acinetobacter spp. isolates. In conclusion, combining LN-1-255 with imipenem, meropenem, cefepime, and sulbactam to target A. baumannii, and especially carbapenem-resistant isolates, represents an attractive option that should be developed for the treatment of infections caused by this pathogen.