A new fault diagnosis model is proposed based on Multi-Class Least Square Support Vector Machine optimized hierarchically by Genetic Algorithm(GA). Original vibration signals are decomposed into several stationary IMFs. Then the instantaneous amplitude energy of the IMFs with fault modulation characteristics is computed and regarded as the input characteristic measure of the Poly-kernel Multi-Class LS-SVM for fault classification. EMD decomposition adaptively isolates the fault modulation signals from original signals. The differences among instantaneous amplitude energy vectors reflect the separability of different fault types. Adopting GA to optimize punish parameter and Poly-kernel parameters hierarchically can not only enhance fault prediction accuracy of Multi-Class LS-SVM with Poly-kernel, but also improve adaptive diagnosis capacity of LS-SVM. The GA-based hierarchical optimization is also applicable to Multi-Class LS-SVM with Lin-kernel, RBF-kernel or Sigmoid-kernel. The deep groove ball bearings fault diagnosis experiment shows the effectivity of this new model.