Complex geometric variations of 3D models usually pose great challenges in 3D shape matching and retrieval. In this paper, we propose a novel 3D shape feature learning method to extract high-level shape features that are insensitive to geometric deformations of shapes. Our method uses a discriminative deep auto-encoder to learn deformation-invariant shape features. First, a multiscale shape distribution is computed and used as input to the auto-encoder. We then impose the Fisher discrimination criterion on the neurons in the hidden layer to develop a deep discriminative auto-encoder. Finally, the outputs from the hidden layers of the discriminative auto-encoders at different scales are concatenated to form the shape descriptor. The proposed method is evaluated on four benchmark datasets that contain 3D models with large geometric variations: McGill, SHREC'10 ShapeGoogle, SHREC'14 Human and SHREC'14 Large Scale Comprehensive Retrieval Track Benchmark datasets. Experimental results on the benchmark datasets demonstrate the effectiveness of the proposed method for 3D shape retrieval.