The detection and tracking of multiple weak targets with time-varying and unknown number has become a hot spot and challenging problem in marine radar application. This paper integrates δ-generalized labeled multi-Bernoulli (δ-GLMB) density and labeled multi-Bernoulli (LMB) density, which are two important special cases of labeled random finite set, to propose an effective method for multiple weak target tracking with track-before-detect strategy based on Bayes framework including prediction and update step. The proposed method can deal with multi-target tracking problem with tractable computational complexity due to prediction step with dynamic grouping procedure albeit with slightly precision loss compared with standard δ-GLMB filter. In general, the conjugate prior property based GLMB does not hold on for generic observation model in update step. In order to solve this problem, this paper applies a tractable principled approximation involving GLMB density, which was firstly proposed in the literature, to make whole Bayes filtering with labeled RFS to perform iteratively for each group with TBD model. Finally, the numerical simulation results of Swerling type 1 target tracking in K-distributed sea clutter illustrate that the proposed method is superior to the methods including standard δ-GLMB-TBD filter, LMB-TBD filter and DP-TBD algorithm in comprehensive performance.