Classification of partially occluded images is a highly challenging computer vision problem even for the cutting edge deep learning technologies. To achieve a robust image classification for occluded images, this paper proposes a novel scheme using subspace decomposition based estimation (SDBE). The proposed SDBE-based classification scheme first employs a base convolutional neural network to extract the deep feature vector (DFV) and then utilizes the SDBE to compute the DFV of the original occlusion-free image for classification. The SDBE is performed by projecting the DFV of the occluded image onto the linear span of a class dictionary (CD) along the linear span of an occlusion error dictionary (OED). The CD and OED are constructed respectively by concatenating the DFVs of a training set and the occlusion error vectors of an extra set of image pairs. Two implementations of the SDBE are studied in this paper: the $l_1$-norm and the squared $l_2$-norm regularized least-squares estimates. By employing the ResNet-152, pre-trained on the ILSVRC2012 training set, as the base network, the proposed SBDE-based classification scheme is extensively evaluated on the Caltech-101 and ILSVRC2012 datasets. Extensive experimental results demonstrate that the proposed SDBE-based scheme dramatically boosts the classification accuracy for occluded images, and achieves around $22.25\%$ increase in classification accuracy under $20\%$ occlusion on the ILSVRC2012 dataset.