Object co-detection aims at simultaneous detection of objects of the same category from a pool of related images by exploiting consistent visual patterns present in candidate objects in the images. The related image set may contain a mixture of annotated objects and candidate objects generated by automatic detectors. Co-detection differs from the conventional object detection paradigm in which detection over each test image is determined one-by-one independently without taking advantage of common patterns in the data pool. In this paper, we propose a novel, robust approach to dramatically enhance co-detection by extracting a shared low-rank representation of the object instances in multiple feature spaces. The idea is analogous to that of the well-known Robust PCA~\cite{rpca}, but has not been explored in object co-detection so far. The representation is based on a linear reconstruction over the entire data set and the low-rank approach enables effective removal of noisy and outlier samples. The extracted low-rank representation can be used to detect the target objects by spectral clustering. Extensive experiments over diverse benchmark datasets demonstrate consistent and significant performance gains of the proposed method over the state-of-the-art object co-detection method and the generic object detection methods without co-detection formulations.