Object proposals are an ensemble of bounding boxes with high potential to contain objects. In order to determine a small set of proposals with a high recall, a common scheme is extracting multiple features followed by a ranking algorithm which however, incurs two major challenges: 1) The ranking model often imposes pairwise constraints between each proposal, rendering the problem away from an efficient training/testing phase; 2) Linear kernels are utilized due to the computational and memory bottleneck of training a kernelized model. In this paper, we remedy these two issues by suggesting a kernelized partial ranking model. In particular, we demonstrate that i) our partial ranking model reduces the number of constraints from O(n) to O(nk) where n is the number of all potential proposals for an image but we are only interested in top-k of them that has the largest overlap with the ground truth; ii) we permit non-linear kernels in our model which is often superior to the linear classifier in terms of accuracy. For the sake of mitigating the computational and memory issues, we introduce a consistent weighted sampling (CWS) paradigm that approximates the non-linear kernel as well as facilitates an efficient learning. In fact, as we will show, training a linear CWS model amounts to learning a kernelized model. Extensive experiments demonstrate that equipped with the non-linear kernel and the partial ranking algorithm, recall at top-k proposals can be substantially improved.