The world is united socially and technologically with means of languages. Hence there is a big requirement for transfer of information from one language to another. Sanskrit is considered as an important language in the Indo-European family. A lot of work is still required to explore the potential of this language to open vistas in the computational linguistic domain. Currently, Sanskrit-Hindi translation system uses rule-based and statistical approaches. These approaches are not adequate for extending the system to generic and huge domains. In order to remove this problem, an efficient system is required to be developed which would cover various domains. Therefore, a hybrid system combining the best of Neural Machine Translation (NMT) and Rule-Based Machine Translation (RBMT) is developed and presented in this paper. The proposed hybrid model has a BLEU score of 61.2% which is higher than other existing systems i.e 41%. This approach uses deep learning feature to overcome drawbacks of the existing systems. Experimental results show that the proposed hybrid system using deep learning model has a high accuracy of 99%. It is also evaluated that it has less response time and more speed than existing systems.