Cognitive flexibility, a vital component of executive function, entails the utilization of extended brain networks. Olfactory stimulation has been shown to influence various brain functions, particularly cognitive performance. To investigate aroma inhalation's effects on brain activity dynamics associated with cognitive flexibility, 20 healthy adults were recruited to complete a set-shifting task during two experimental conditions: no aroma stimuli vs. lavender essential oil inhalation. Using Thomson's multitaper approach, the normalized power spectral density (NPSD) was assessed for five frequency bands. Findings confirm that aroma inhalation significantly affects behavioral indices (i.e., reaction time (RT) and response accuracy) and electroencephalogram (EEG) signatures, especially in the frontal lobe. Participants showed a tremendous increase in theta and alpha NPSD, associated with relaxation, along with beta NPSD, associated with clear and fast thinking after inhaling the aroma. NPSD of the delta band, an indicator of the unconscious mind, significantly decreased when stimulated with lavender essential oil. Further, participants exhibited shorter RT and more accurate responses following aroma inhalation. Our findings revealed significant changes in oscillatory power and behavioral performance after aroma inhalation, providing neural evidence that olfactory stimulation with lavender essential oil may facilitate cognitive flexibility.