Replacing the petroleum-based materials in the food industry is one of the main objectives of the scientists and decision makers worldwide. Biodegradable packaging will help diminish the environmental impact of human activity. Improving such biodegradable packaging materials by adding antimicrobial activity will not only extend the shelf life of foodstuff, but will also eliminate some health hazards associated with food borne diseases, and by diminishing the food spoilage will decrease the food waste. The objective of this research was to obtain innovative antibacterial films based on a biodegradable polymer, namely alginate. Films were characterized by environmental scanning electron microscopy (ESEM), Fourier-transform infrared spectroscopy (FTIR) and microscopy, complex thermal analysis (TG-DSC-FTIR), UV-Vis and fluorescence spectroscopy. Water vapor permeability and swelling behavior were also determined. As antimicrobial agents, we used silver spherical nanoparticles (Ag NPs) and lemongrass essential oil (LGO), which were found to act in a synergic way. The obtained films exhibited strong antibacterial activity against tested strains, two Gram-positive (Bacillus cereus and Staphylococcus aureus) and two Gram-negative (Escherichia coli and Salmonella Typhi). Best results were obtained against Bacillus cereus. The tests indicate that the antimicrobial films can be used as packaging, preserving the color, surface texture, and softness of cheese for 14 days. At the same time, the color of the films changed (darkened) as a function of temperature and light presence, a feature that can be used to monitor the storage conditions for sensitive food.