Object recognition is a fundamental problem in many video processing tasks, accurately locating seen objects at low computation cost paves the way for on-device video recognition. We propose PatchNet, an efficient convolutional neural network to match objects in adjacent video frames. It learns the patchwise correlation features instead of pixel features. PatchNet is very compact, running at just 58MFLOPs, $5\times$ simpler than MobileNetV2. We demonstrate its application on two tasks, video object detection and visual object tracking. On ImageNet VID, PatchNet reduces the flops of R-FCN ResNet-101 by 5x and EfficientDet-D0 by 3.4x with less than 1% mAP loss. On OTB2015, PatchNet reduces SiamFC and SiamRPN by 2.5x with no accuracy loss. Experiments on Jetson Nano further demonstrate 2.8x to 4.3x speed-ups associated with flops reduction. Code is open sourced at https://github.com/RalphMao/PatchNet.