The performance of a fiber Bragg grating strain sensor constructed with 3$ imes$3 coupler is investigated. A 3$ imes$3 coupler Mach-Zehnder (M/Z) interferometer is used as wavelength discriminator, interrogating strain-induced Bragg wavelength shifts. Two quadrature-phase-shifted intensities are synthesized from the as-coupled interferometer outputs, and digital arctangent demodulation and phase unwrapping algorithm are applied to extract the phase information proportional to strain. Due to the linear relation between the input strain and the output of quadrature signal processing, signal-fading problems eliminated. In the experiment, a fiber grating that was surface adhered on an aluminum beam was strained in different ways, and the photodetector signals were transferred and processed in a computer-controlled processing unit. A phase recovery fo 7.8$pi$ pk-pk excursion, which corresponds to ~650$mu$strain pk-pk of applied strain, was demonstrated. The sensor system was stable over the environmental intensi쇼 perturbations because of the self-referencing effect in the demodulation process.