Due to the merits of high efficiency and strong security against timing and side-channel attacks, ChaCha has been widely applied in real-time communication and data streaming scenarios. However, with the rapid development of AI-assisted cryptanalysis and quantum computing technologies, there are serious challenges to the secure implementation of ChaCha cipher. To further strengthen the security of ChaCha cipher, we propose an improved variant based on quantum random numbers, i.e., Quantum Random Number Enhanced ChaCha (QRE-ChaCha). Specifically, the design XORs the initial constants with quantum random numbers and periodically injects quantum random numbers into selected state words during odd rounds to enhance diffusion. Compared with the original ChaCha, the present variant shows stronger resistance to differential attacks and generates a keystream with statistical randomness, thereby offering increased robustness against both classical and quantum attacks. To evaluate the security and performance of the present ChaCha, our analysis proceeds in three main parts. Firstly, we analyze its theoretical security in terms of quantum randomness and attack testing, and conduct differential cryptanalysis with an automated search method based on the Boolean satisfiability problem (SAT). Secondly, we subject the keystream generated by the cipher to randomness tests using the NIST statistical test suite and the GM/T 0005-2021 randomness testing standard. Finally, we assess its encryption and decryption performance by measuring its encryption speed on files of various sizes. According to the results, the present ChaCha is significantly improved to resist differential attacks while maintaining the high efficiency of the original ChaCha cipher, and its keystream successfully passes statistical randomness tests using the NIST and GM/T 0005-2021 standards, meeting cryptographic application requirements.