Fiber Bragg grating sensing principle is based on the exact tracking of the peak wavelength location. Several peak detection techniques have already been proposed in literature. Among these, conventional peak detection (CPD) methods such as the maximum detection algorithm (MDA), do not achieve very high precision and accuracy, especially when the Signal to Noise Ratio (SNR) and the wavelength resolution are poor. On the other hand, recently proposed algorithms, like the cross-correlation demodulation algorithm (CCA), are more precise and accurate but require higher computational effort. To overcome these limitations, we developed a novel fast phase correlation algorithm (FPC) which performs as well as the CCA, being at the same time considerably faster. This paper presents the FPC technique and analyzes its performances for different SNR and wavelength resolutions. Using simulations and experiments, we compared the FPC with the MDA and CCA algorithms. The FPC detection capabilities were as precise and accurate as those of the CCA and considerably better than those of the CPD. The FPC computational time was up to 50 times lower than CCA, making the FPC a valid candidate for future implementation in real-time systems.