In this paper, an optical absorption based fiber optic surface plasmon resonance (SPR) sensor has been studied theoretically. The theoretical treatment is based on Kretschmann’s SPR theory and the Lorentz model that expresses a damped harmonic oscillator is included in the treatment for optical absorption in the sensing layer. The optical source considered is an un-polarized collimated beam. The light is coupled to the fiber using a microscope objective that focuses the beam at the center of the input face of the fiber. The effects of the parameters related to the sensing region, the light source and the optical fiber on the sensitivity and the operating range of the SPR sensor have been studied with the help of numerical calculations and computer simulations. It has been found that the excitation frequency in absorption-based fiber optic SPR sensor is an important parameter. The sensitivity is better for the lower off-resonance excitation frequency. The sensitivity and the operating range of the sensor are better for large value of the core diameter. The optimization of numerical aperture of the fiber, film thickness and the length of the sensing region is required to achieve the maximum sensitivity. Further, the increase in the extinction coefficient of the sample increases the sensitivity of the sensor while the decrease in the width of its absorption spectrum increases the sensitivity. The sensitivity and the operating range of the sensor are better for small values of the refractive index of the absorbing sample.