A simple cost-effective laser-induced breakdown spectroscopy (LIBS) instrument was used for quantification of major elements in several nickel alloys and also sorting them. A compact low-power diode-pumped solid-state laser and a miniature low-resolution spectrometer were assembled for the LIBS instrument. Material properties of the nickel alloys depend mainly on the composition of the major elements, Ni, Cr, and Fe, ranging from a few to ∼60 wt%. The emission peaks at 547.7 nm, 520.4 nm, and 438.1 nm for Ni, Cr, and Fe, respectively, were chosen for this analysis. The analytical performance was found to be enough for the quantification of Ni, Cr, and Fe in the nickel alloys. Limits of detection and accuracy were estimated to be a few weight percent (wt%) and measurement precisions were less than 10% in terms of relative standard deviation. The calibration performance of this intensity-based method was compared with that of the "ratio method" which is used in conventional optical emission spectroscopy analyses. The comparison indicates that the intensity-based method is more appropriate with the low-performance LIBS instrument that detects emission peaks of only a few major elements. Also, multivariate modeling of the six different nickel alloy samples based on the emission peak intensities of Ni, Cr, and Fe was performed using k-nearest neighbors (KNN) and linear discriminant analysis (LDA). The KNN and ordinary LDA models showed 95.0% and 98.3% classification correctness for the separate test data set, respectively. To improve classification performance further, the two-step LDA model was trained. In this approach, the two closest sample classes responsible for the decrease in the classification correctness were separately modeled in the second step to exploit their difference effectively. The two-step LDA model showed 100% correctness in classifying the test objects. Our results indicate that such a low-performance LIBS instrument can be effectively utilized for quantitative analysis of the major elements in the nickel alloys and their rapid identification or sorting in combination with an appropriate multivariate modeling algorithm.