In spite of advances in object recognition technology, Handwritten Bangla Character Recognition (HBCR) remains largely unsolved due to the presence of many ambiguous handwritten characters and excessively cursive Bangla handwritings. Even the best existing recognizers do not lead to satisfactory performance for practical applications related to Bangla character recognition and have much lower performance than those developed for English alpha-numeric characters. To improve the performance of HBCR, we herein present the application of the state-of-the-art Deep Convolutional Neural Networks (DCNN) including VGG Network, All Convolution Network (All-Conv Net), Network in Network (NiN), Residual Network, FractalNet, and DenseNet for HBCR. The deep learning approaches have the advantage of extracting and using feature information, improving the recognition of 2D shapes with a high degree of invariance to translation, scaling and other distortions. We systematically evaluated the performance of DCNN models on publicly available Bangla handwritten character dataset called CMATERdb and achieved the superior recognition accuracy when using DCNN models. This improvement would help in building an automatic HBCR system for practical applications.