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In this work we present an analysis of the response of a compact, simple and inexpensive optoelectronic sensor system intended to detect spectral shifts of a long-period fiber grating (LPG). The system makes use of a diffraction grating and a couple of receiving optical fibers that pick up signals at two different wavelengths. This differential detection system provides the same useful information from an LPG-based sensor as with a conventional laboratory system using optical spectrum analyzers for monitoring the minimum offset of LPG. The design of the fiber detection pair as a function of the parameters of the dispersion grating, the pick-up fiber and the LPG parameters, is presented in detail. Simulation of the detection system responses is presented using real from spectral shifts in nano-coated LPGs caused by the evaporation of various liquids such as water, ethanol and acetone, which are examples of corrosive, flammable and hazardous substances. Fiber optic sensors with similar detection can find applications in structural health monitoring for moisture detection, monitoring the spillage of toxic and flammable substances in industry etc.