Sub-Nyquist radars require fewer measurements, facilitating low-cost design, flexible resource allocation, etc. By applying compressed sensing (CS) method, such radars achieve close performance to traditional Nyquist radars. However in low signal-to-noise ratio (SNR) scenarios, detecting weak targets is challenging: low probability of detection and many spurious targets could occur in the recovery results of traditional CS method. To overcome this issue, we propose a weighted sparse recovery based track-before-detect (TBD) method for weak targets detection by accumulating multi-frame information. Particularly, tracking results of targets are utilized as prior knowledge to enhance the recovery accuracy, thus improving the detection performance. Numerical results show that our method improves the detection performance particularly and reduces the occurrence of spurious targets in low SNR situations compared with
traditional CS method.