It is critical for normal brains to perceive the external world precisely and accurately under ever-changing operational conditions, yet the mechanisms underlying this fundamental brain function in the sensory systems are poorly understood. To address this issue in the olfactory system, we investigated the responses of olfactory bulbs to odor stimulations under different brain states manipulated by anesthesia levels. Our results revealed that in two brain states, where the spontaneous baseline activities differed about twofold based on the local field potential (LFP) signals, the levels of neural activities reached after the same odor stimulation had no significant difference. This phenomenon was independent of anesthetics (pentobarbital or chloral hydrate), stimulating odorants (ethyl propionate, ethyl butyrate, ethyl valerate, amyl acetate, n-heptanal, or 2-heptanone), odor concentrations, and recording sites (the mitral or granular cell layers) for LFPs in three frequency bands (12-32 Hz, 33-64 Hz, and 65-90 Hz) and for multiunit activities. Furthermore, the activity patterns of the same stimulation under these two brain states were highly similar at both LFP and multiunit levels. These converging results argue the existence of mechanisms in the olfactory bulbs that ensure the delivery of peripheral olfactory information to higher olfactory centers with high fidelity under different brain states.