Fiber lasers are characterized by high efficiency, good beam quality, and high reliability and are widely used in industries. In addition, the high repetition frequency of fiber lasers can increase the analytical efficiency greatly. In this paper, a nanosecond fiber laser was introduced to be the ablation source in laser-induced breakdown spectroscopy (LIBS) for determining copper, magnesium, and manganese in aluminum alloys. Because of the high repetition frequency of the fiber laser, the conventional delay-acquisition strategy was unavailable. Discrete wavelet transform (DWT) was used to mitigate the interference of the Bremsstrahlung background. Standard calibration and internal calibration methods were also compared for quantitative analyses. The results demonstrated that the combination of DWT and internal calibration effectively improved the analytical accuracy. After optimization, the R2s of the FL-LIBS system for Cu, Mg, and Mn were 0.9897, 0.9964, and 0.9979, respectively; the root mean squared error of cross validation was 0.0414, 0.0462, and 0.031 wt. %, respectively. This study provides a convenient method for the rapid elemental analysis of aluminum alloys.