The chemical composition, including the enantiomeric excess of the main terpenes, of essential oils from seeds and cones of Abies concolor was studied by chromatographic (GC) and spectroscopic methods (mass spectrometry, nuclear magnetic resonance), leading to the determination of 98 compounds. Essential oils were mainly composed of monoterpene hydrocarbons. The dominant volatiles of seed essential oil were: limonene (47 g/100 g, almost pure levorotary form) and α-pinene (40 g/100 g), while α-pinene (58 g/100 g), sabinene (11 g/100 g), and β-pinene (4.5 g/100 g) were the predominant components of the cone oil. The seed and cone essential oils exhibited mild antibacterial activity, and the MIC ranged from 26 to 30 μL/mL against all of the tested bacterial standard strains: Staphylococcus aureus, Enterococcus faecalis, Enterococcus faecium, Escherichia coli, and Klebsiella pneumoniae. The cytotoxic studies have demonstrated that tested essential oils were cytotoxic to human skin fibroblasts and human microvascular endothelial cells at concentrations much lower than the MIC. The essential oils from A. concolor seeds and cones had no toxic effect on human skin fibroblasts and human microvascular endothelial cells, when added to the cells at a low concentration (0–0.075 μL/mL) and (0–1.0 μL/mL), respectively, and cultured for 24 h.