The triangulation method has been an effective tool for estimating the source locations of various acoustic emissions (AE). However, it is hard to guarantee high accuracy in composite structures due to their anisotropy. Also, the conventional methods basically require the precise arrival time data of AE signals. Because most of commercial fiber optic sensing systems applicable to real structures have limited measurement performance, the arrival times cannot be clearly identified. In this paper, the magnitudes of fiber optic sensor signals were used for estimating the distances between each sensor and impact location. In order to obtain higher correlation between the magnitude and distance, the signal near the roughly estimated arrival time was used for calculating the magnitude. Then, through the neural network training, the accuracy of estimating the distances from the signal magnitudes could be enhanced. Finally, the triangulation method was applied for localizing the impact sources. As a result, our suggested triangulation method showed the acceptable localization results about the non-trained impact points. Because the input data for this method could be reliably obtained from the commercial fiber optic sensing system, it can be useful for constructing a simple impact monitoring system for the real composite structures.