In this paper, a real-time underwater robotic visual tracking strategy (RUTS) based on underwater image restoration and Kernelized Correlation Filters (KCF) is developed for underwater robots. A real-time and unsupervised advancement scheme (RUAS), which is utilized in this strategy, performs robustly in restoring underwater images. The KCF, as a high-speed and accurate tracking method on land, is employed in this strategy. To handle the conflict between tracking speed and accuracy, we propose a tracking strategy based on KCF in video sequence restored by RUAS, comparing Histogram of Oriented Gradient (HOG) descriptors and raw pixels gray (RPG) descriptors. We define an index Ac to describe the tracking accuracy and regard the number of frames per second as computing speed. Results of contrast experiments show that the RPG, a much simpler descriptor, can achieve tracking accuracy as precise as HOG, accompanied by an increase of tracking speed up to 36%. Finally, experiments of the KCF-based tracker with RPG on different underwater objects demonstrate the feasibility of the formed RUTS.