Piwi interacting RNA (piRNA) molecules belong to a largest class of small non coding RNA molecules which are originally discovered in animal germline cells and also occur across a variety of human somatic cells. The piRNA molecules play a significant role in many gene functions such as protecting genomic integrity, gene expression regulation and restricting the functions of transposable elements. The identification of piRNA molecules and their function types are significant for cancer cells diagnosis, drug developments and genes stability. A number of traditional machine learning methods have been proposed for identification of piRNAs and their functions. However, these methods are required a considerable amounts of human engineering and expertise to design an accurate identification model. Hence, this paper proposes a two level computational model based on deep neural network (DNN) that automatically extract informative features from RNA sequences using standard learning methods. Moreover, the proposed model employs di-nucleotide auto covariance (DAC) method along with six physiochemical properties to construct a feature vector. The performance of the proposed model has been extensively evaluated through k-fold cross-validation tests. Firstly, the performance of the proposed model is compared with commonly used classifier algorithms using benchmark dataset. Secondly, its performance is compared with the existing state-of- the-art computational models. The experimental results show that the proposed model performed better than the existing predictors with accuracy level 91.81% and 84.52% in the first level and in the second level respectively. The source code along with dataset of the proposed model is freely available at https://github.com/salman-khan-mrd/2L-piRNADNN.