Silicon photonic crystal sensors have become very attractive for various optical sensing applications. Using silicon as a material platform provides the ability to fabricate sensors with other photonic devices on a single chip. In this paper, a new optical sensor based on optical resonance in a one-dimensional silicon photonic crystal with an air defect is theoretically studied for refractive index sensing in the infrared wavelength region. The air defect introduces a cavity into the photonic crystal, making it suitable for probing the properties of a gas found within the cavity. This photonic crystal nanocavity is designed to oscillate at a single mode with a high quality factor, allowing for refractive index sensing of gases with a high sensitivity. A method is presented to maximize the sensitivity of the sensor and to obtain a very narrow bandwidth cavity mode for good sensor resolution. We change the thickness of the air layers linearly in the photonic crystals on both sides of the nanocavity and show that a sensitivity of 1200 nm RIU⁻¹ can be achieved. We present a detailed analysis of the sensor and variations of the layer thicknesses, the cavity length, and the number of periodic layers in the photonic crystal are investigated. This optical sensor has a much simpler design and higher sensitivity compared to other photonic crystal sensors reported previously.