It is challenging to track a target continuously in videos with long-term occlusion,or objects which leave then re-enter a scene.Existing tracking algorithms combined with onlinetrained object detectors perform unreliably in complex conditions, and can only provide discontinuous trajectories with jumps in position when the object is occluded. This paper proposes a novel framework of tracking-by-detection using selection and completion to solve the abovementioned problems. It has two components, tracking and trajectory completion. An offline-trained object detector can localize objects in the same category as the object being tracked. The object detector is based on a highly accurate deep learning model. The object selector determines which object should be used to re-initialize a traditional tracker. As the object selector is trained online,it allows the framework to be adaptable. During completion, a predictive non-linear autoregressive neural network completes any discontinuous trajectory.The tracking component is an online real-time algorithm, and the completion part is an after-theevent mechanism. Quantitative experiments show a significant improvement in robustness over prior stateof-the-art methods.