This paper presents a novel nonparametric backpropagation Bayesian compressive sensing (BBCS) classification approach. While the state-of-the-art parametric classifiers such as logistic regression re-quire model training and can result in inadequate models, the developed approach does not require model training. It is combined with a column-based subspace sampling process and can deal efficiently with uncertainties and highly computational tasks. Validation on a publicly available vehicle logo dataset shows that the proposed classifier can achieve up to 98% recognition accuracy as compared with the state-of-the-art nonparametric classifiers. Compared with the generic Bayesian compressive sensing classification, the proposed approach decreases the mean number of misclassifications by 87% along with 68% reduction of the computational time. The robustness of the BBCS approach is demonstrated over scene recognition tasks, and its outperformance over the AlexNet convolutional neural network algorithm is demonstrated in noisy conditions. The proposed BBCS approach is generic and can be used in different areas; for example, it has shown robustness over the CIFAR-10 dataset.