Locating low-velocity impacts (LVIs) on composite plates precisely is necessary. Support vector regression (SVR) is an effective method in addressing the LVI localization problem, whereas a large number of impact features may lead to a slow computational rate and over-fitting of the SVR model. In this paper, a binary dynamic stochastic search algorithm (BDSS) is proposed by introducing a threshold factor and the encoding concept of genetic algorithm into the original dynamic stochastic search algorithm (DSS). Then, a feature selection method is proposed by combining BDSS with SVR, which is called BDSS-SVR. BDSS-SVR as a wrapper method can simultaneously implement dimensionality reduction of impact features and optimize the SVR model’s parameters. Furthermore, a novel LVI localization method based on BDSS-SVR and multi-domain features is designed for accurately detecting the LVIs on a carbon fiber reinforced plastic (CFRP) plate. To analyze the performance of BDSS-SVR, a LVI localization system based on fiber Bragg grating (FBG) sensors is applied to the conduction of two experiments. Two additional control parameters of BDSS-SVR, including the threshold factor and weight coefficient, are tuned in the first experiment. Moreover, the statistical results in the second experiment illustrate that BDSS-SVR outperforms optimized SVR using DSS, feature selection methods based on five state-of-the-art algorithms and SVR, and five machine learning methods. For fifteen random LVIs on the CFRP plate, BDSS-SVR effectively reduces the number of impact features and provides satisfactory localization accuracy. The maximum, minimum, and average errors are 4.659 mm, 0.024 mm, and 3.065 mm, respectively.