The article introduces a new method called Efficient Mixed-Model Association (EMMA) for correcting population structure and genetic relatedness in association mapping studies of model organisms. EMMA addresses the issue of inflated false positive rates in genetic association studies of inbred strains, which is common due to complex population structures. Traditional methods like genomic control and structured association are inadequate for model organisms, while mixed models can effectively correct for these issues. However, existing mixed-model implementations are computationally inefficient. EMMA improves computational efficiency by leveraging spectral decomposition, reducing the complexity from cubic to linear time per iteration. It also ensures the positive semidefiniteness of the kinship matrix, enhancing the reliability of results. The method is applied to maize, Arabidopsis, and mouse data sets, demonstrating its ability to identify significant associations while reducing false positives. Simulation studies show that EMMA can achieve high statistical power with multiple measurements per strain, even with limited inbred strains. The R package and webserver for EMMA are publicly available.The article introduces a new method called Efficient Mixed-Model Association (EMMA) for correcting population structure and genetic relatedness in association mapping studies of model organisms. EMMA addresses the issue of inflated false positive rates in genetic association studies of inbred strains, which is common due to complex population structures. Traditional methods like genomic control and structured association are inadequate for model organisms, while mixed models can effectively correct for these issues. However, existing mixed-model implementations are computationally inefficient. EMMA improves computational efficiency by leveraging spectral decomposition, reducing the complexity from cubic to linear time per iteration. It also ensures the positive semidefiniteness of the kinship matrix, enhancing the reliability of results. The method is applied to maize, Arabidopsis, and mouse data sets, demonstrating its ability to identify significant associations while reducing false positives. Simulation studies show that EMMA can achieve high statistical power with multiple measurements per strain, even with limited inbred strains. The R package and webserver for EMMA are publicly available.