Extreme learning machine (ELM), as a kind of single hidden layer feedforword neural networks, is an important tool in big data analysis. Compared with traditional neural network methods, it has simple structure, high learning speed and good generalization performance. However, the output weight of ELM is estimated by the least squares estimation (LSE) method, and thus ELM network lacks of robustness since LSE is relatively sensitive to outlier. A new robust ELM based on least absolute deviations (LAD) regression, called LAD-ELM, is presented. Moreover, the proposed LAD-ELM is posed as a linear program with global optimal solution. Furthermore, the proposed LAD-ELM is directly used for near-infrared (NIR) spectral analysis, and an analysis system for hardness of licorice seeds is built based on LAD-ELM and NIR data. Compared with the traditional methods, the experimental results in different spectral regions show the feasibility and effectiveness of the proposed method. Moreover, the investigation provides theoretical support and practical method for studies on licorice seed hardness using ELM and NIR technology.