With the rapid development of information and communication technologies, the informatization of modern society is gaining momentum. Cryptography is one of the technologies that support the infor- mation society. Cryptography is essential for maintaining the confidentiality, integrity, and availability of electronic data. Cryptographic techniques include symmetric-key cryptography, in which the encryp- tion key and decryption key are the same, and public-key cryptography, in which the encryption key and decryption key are different. Compared to public-key cryptography, symmetric-key cryptography is faster in data processing speed, and is used for processing big data. However, it is difficult to prove the security of symmetric-key cryptography, and vulnerability analysis is widely used to improve the security of cryptography. The differential analysis method has been widely used to analyze ChaCha, one of the symmetric key ciphers selected for TLS 1.3. Differential analysis is a method that focuses on the probability bias between the input and output differentials of a cryptosystem. Recently, a new method called linear differential analysis has been proposed, which combines differential analysis with linear analysis using linear relationships between states before and after state transitions. In this study, we derived a new linear relation for ChaCha and experimentally demonstrated a higher probability bias. We also found input/output difference combinations corresponding to the new linear relation and exper- imentally showed their probability biases. We also show that the proposed bias can be used to attack 7-round ChaCha with a reduced computational complexity from 2^221.95 to 2^132, improving on the smallest computational complexity of the existing analysis for ChaCha.