In this paper, we consider the animal object detection and segmentation from wildlife monitoring videos captured by motion-triggered cameras, called camera-traps. For these types of videos, existing approaches often suffer from low detection rates due to low contrast between the foreground animals and the cluttered background, as well as high false positive rates due to the dynamic background. To address this issue, we first develop a new approach to generate animal object region proposals using multilevel graph cut in the spatiotemporal domain. We then develop a cross-frame temporal patch verification method to determine if these region proposals are true animals or background patches. We construct an efficient feature description for animal detection using joint deep learning and histogram of oriented gradient features encoded with Fisher vectors. Our extensive experimental results and performance comparisons over a diverse set of challenging camera-trap data demonstrate that the proposed spatiotemporal object proposal and patch verification framework outperforms the state-of-the-art methods, including the recent Faster-RCNN method, on animal object detection accuracy by up to 4.5%.