Monitoring the antibiotic resistance of H. pylori is an important step in the effective treatment of this bacterium, thus the aim of the present study was to assess the prevalence of antimicrobial resistance of H. pylori strains isolated from pediatric and adult patients with primary infections in 2016–2018. Antral biopsies from 334 treatment-naïve patients (126 children and 208 adults) were obtained. A total of 71 clinical H. pylori strains (22 from children and 49 from adults) were isolated and examined for amoxicillin (AMX), clarithromycin (CLR), metronidazole (MTZ), tetracycline (TET), and levofloxacin (LEV) susceptibility. The activity of the antibiotics was measured by E-tests. Strains were considered as resistant to antibiotics with minimum inhibitory concentrations (MICs) equal to ≥0.125 μg/mL (AMX), ≥0.5 μg/mL (CLR), ≥8 μg/mL (MTZ), and ≥1 μg/mL (TET and LEV). The highest prevalence of antibiotic resistance in H. pylori strains was observed for CLR and MTZ, at frequencies of 54.5% and 31.8% vs. 30.6% and 46.9% for children and adults, respectively. A much lower frequency of isolation of resistant strains was demonstrated for LEV and TET, this being 9.1% and 4.5% vs. 18.4% and 4.1% for pediatric and adult patients, respectively. The presence of AMX-resistant strains was not observed. The H. pylori strains isolated from Polish patients with primary infections showed a high level of antibiotic resistance to CLR and MTZ (>30%).