Identification and discrimination of bacterial strains of same species exhibiting resistance to antibiotics using Laser Induced Breakdown Spectroscopy (LIBS) and Neural Networks (NN) algorithm is reported. The method has been applied to identify 40 bacterial strains causing Hospital Acquired Infections (HAI), i.e. Pseudomonas aeruginosa, Escherichia coli, Klebsiella pneumoniae, Salmonella typhimurium, Salmonella pullurum and Salmonella salamae. The strains analyzed included both isolated from clinical samples and constructed in laboratory that differ in mutations as a result of their resistance to one or more antibiotics. Small changes in the atomic composition of the bacterial strains, as a result of their mutations and genetic variations, were detected by the LIBS-NN methodology and led to their identification and classification. This is of utmost importance because solely identification of bacterial species is not sufficient for disease diagnosis and identification of the actual strain is also required. The proposed method was successfully able to discriminate strains of the same bacterial species. The optimized NN models provided reliable bacterial strain identification with an index of spectral correlation higher than 95% for the samples analyzed, showing the potential and effectiveness of the method to address the safety and social-cost HAI-related issue.