In this paper, we propose what we believe is a novel sensitive micro-optoelectromechanical systems (MOEMS) accelerometer based on intensity modulation by using a one-dimensional photonic crystal. The optical sensing system of the proposed structure includes an air-dielectric multilayer photonic bandgap material, a laser diode (LD) light source, a typical photodiode (1550 nm) and a set of integrated optical waveguides. The proposed sensor provides several advantages, such as a relatively wide measurement range, good linearity in the whole measurement range, integration capability, negligible cross-axis sensitivity, high reliability, and low air-damping coefficient, which results in a wider frequency bandwidth for a fixed resonance frequency. Simulation results show that the functional characteristics of the sensor are as follows: a mechanical sensitivity of 119.21 nm/g, a linear measurement range of ±38g and a resonance frequency of 1444 Hz. Thanks to the above-mentioned characteristics, the proposed MOEMS accelerometer is suitable for a wide spectrum of applications, ranging from consumer electronics to aerospace and inertial navigation.