Integrative multi-omics analysis provides deeper insight and enables better and more realistic modeling of the underlying biology and causes of diseases than does single omics analysis. Although several integrative multi-omics analysis methods have been proposed and demonstrated promising results in integrating distinct omics datasets, inconsistent distribution of the different omics data, which is caused by technology variations, poses a challenge for paired integrative multi-omics methods. In addition, the existing discriminant analysis-based integrative methods do not effectively exploit correlation and consistent discriminant structures, necessitating a compromise between correlation and discrimination in using these methods. Herein we present PAN-omics Discriminant Analysis (PANDA), a joint discriminant analysis method that seeks omics-specific discriminant common spaces by jointly learning consistent discriminant latent representations for each omics. PANDA jointly maximizes between-class and minimizes within-class omics variations in a common space and simultaneously models the relationships among omics at the consistency representation and cross-omics correlation levels, overcoming the need for compromise between discrimination and correlation as with the existing integrative multi-omics methods. Because of the consistency representation learning incorporated into the objective function of PANDA, this method seeks a common discriminant space to minimize the differences in distributions among omics, can lead to a more robust latent representations than other methods, and is against the inconsistency of the different omics. We compared PANDA to 10 other state-of-the-art multi-omics data integration methods using both simulated and real-world multi-omics datasets and found that PANDA consistently outperformed them while providing meaningful discriminant latent representations. PANDA is implemented using both R and MATLAB, with codes available at https://github.com/WuLabMDA/PANDA.