Radar multitarget tracking in a dense clutter environment remains a complex problem to be solved. Most existing solutions still rely on complex motion models and prior distribution knowledge. In this paper, a new online tracking method based on a long short-term memory (LSTM) network is proposed. It combines state prediction, measurement association, and trajectory management functions in an end-to-end manner. We employ LSTM networks to model target motion and trajectory associations, relying on their strong learning ability to learn target motion properties and long-term dependence of trajectory associations from noisy data. Moreover, to address the problem of missing appearance information of radar targets, we propose an architecture based on the LSTM network to calculate similarity function by extracting long-term motion features. And the similarity is applied to trajectory associations to improve their robustness. Our proposed method is validated in simulation scenarios and achieves good results.