Brillouin scattering-based distributed optical fiber sensors have been successfully employed in various applications in recent decades, because of benefits such as small size, light weight, electromagnetic immunity, and continuous monitoring of temperature and strain. However, the data processing requirements for the Brillouin Gain Spectrum (BGS) restrict further improvement of monitoring performance and limit the application of real-time measurements. Studies using Feedforward Neural Network (FNN) to measure Brillouin Frequency Shift (BFS) have been performed in recent years to validate the possibility of improving measurement performance. In this work, a novel FNN that is 3 times faster than previous FNNs is proposed to improve BFS measurement performance. More specifically, after the original Brillouin Gain Spectrum (BGS) is preprocessed by Principal Component Analysis (PCA), the data are fed into the Feedforward Neural Network (FNN) to predict BFS.