In this paper, we propose a method to estimate statistical divergence between probability distributions by a DNN-based discriminative approach and its use for language identification tasks. Since statistical divergence is generally defined as a functional of two probability density functions, these density functions are usually represented in a parametric form. Then, if a mismatch exists between the assumed distribution and its true one, the obtained divergence becomes erroneous. In our proposed method, by using Bayes' theorem, the statistical divergence is estimated by using DNN as discriminative estimation model. In our method, the divergence between two distributions is able to be estimated without assuming a specific form for these distributions. When the amount of data available for estimation is small, however, it becomes intractable to calculate the integral of the divergence function over all the feature space and to train neural networks. To mitigate this problem, two solutions are introduced; a model adaptation method for DNN and a sampling approach for integration. We apply this approach to language identification tasks, where the obtained divergences are used to extract a speech structure. Experimental results show that our approach can improve the performance of language identification by 10.85 relative compared to the conventional approach based on i-vector.