The Long Short-Term Memory (LSTM) neural network based data association algorithm named as DeepDA for multi-target tracking in clutters is proposed to deal with the NP-hard combinatorial optimization problem in this paper. Different from the classical data association methods involving complex models and accurate prior knowledge on clutter density, filter covariance or associated gating etc, data-driven deep learning methods have been extensively researched for this topic. Firstly, data association mathematical problem for multitarget tracking on unknown target number, missed detection and clutter, which is beyond one-to-one mapping between observations and targets is redefined formally. Subsequently, an LSTM network is designed to learn the measurement-to-track association probability from radar noisy measurements and exist tracks. Moreover, an LSTM-based data-driven deep neural network after a supervised training through the BPTT and RMSprop optimization method can get the association probability directly. Experimental results on simulated data show a significant performance on association ratio, target ID switching and time-consuming for tracking multiple targets even they are crossing each other in the complicated clutter environment.