Numerous researchers are now concentrating on the English course on intercultural communication. Notwithstanding, these courses encounter several obstacles, including student variations in traditional English for cross-cultural instruction, developing students' cross-cultural communication skills, and improving the quality of instruction. To overcome these problems, in this manuscript, a Hamiltonian deep neural network (NN) approach is proposed for improving the teaching quality of massive open online course (MOOCs) based English course. Initially, data is given from English-language massive open online courses (MOOCs) teaching adult basic life support (ABLS) dataset. Afterward the data is fed to Switching Hierarchical Gaussian Filter. The pre-processing output is provided to the Hamiltonian Deep Neural Network (HDNN) used to improve the teaching quality of MOOC English course. The learnable of the optimized is using Coati Optimization Algorithm (COA). The proposed technique is executed in Python and the effectiveness of the proposed MOOCEC-HDNN method is improved by using various performances evaluating metrics like, teaching Efficiency, Robustness Gain, teaching quality and system Efficiency are analysed. The proposed MOOCEC-HDNN method is shows the higher teaching efficiency of 78%, Robustness Gain of 28dB and teaching quality 68% while comparing other existing methods such as massive open online course (MOOCs) based English course based on Gannet algorithm and Neural Network (MOOCEC-GA-NN), MOOCs based English course based on K-modes algorithm and Neural Network (MOOCEC-KMA-NN) and MOOCs based English course based on Conventional Neural Network (MOOCEC-CNN), respectively.