Joint detection and tracking of weak underwater targets are challenging problems whose complexity is intensified when the target is disturbed by reverberation. In the low signal-to-reverberation ratio (SRR) environment, the traditional detection and tracking methods perform poorly in tracking robustness because they only consider the target motion characteristics. Recently, the kernel correlation filter (KCF) based on target features has received lots of attention and gained great success in visual tracking. We propose an improved multi-kernel correlation filter (IMKCF) tracking-by-detection algorithm by introducing the KCF into the field of underwater weak target detection and tracking. It is composed of the tracking-by-detection, the adaptive reliability check, and the re-detection modules. Specifically, the tracking-by-detection part is built on the multi-kernel correlation filter (MKCF), and it uses multi-frame data weighted averaging to update. The reliability check helps keep the tracker from corruption. The re-detection module, integrated with a Kalman filter, identifies target positions when the tracking is unreliable. Finally, the experimental data processing and analysis show that the proposed method outperforms the single-kernel methods and some traditional tracking methods.