In a global environment, the impact of a company's brand image and reputation on customers' beliefs, attitudes and behaviors becomes a critical issue. For banks, the strength of image and reputation has quickly become a crucial leverage for differentiation and success. In addition, the banking industry is sensitive to risks, especially in the digital environment. Customer's trust is a key factor affecting the decision to make transactions with banks and customer loyalty. This study is to examine the relationship between bank image and reputation, customer's trust, and loyalty. The study was conducted for commercial banks in Ho Chi Minh City. The results show the bank's brand image and reputation have a direct positive impact on customer loyalty. At the same time, customer trust plays a mediating role in this relationship. In addition, this study affirms that the determinants of image and reputation are core services, communication, chief executive reputation, responsiveness, social responsibility, and quality of human resources of banks. The components of customer trust are calculus-based trust, knowledge-based trust and identity-based trust from the perspective of Shapiro, Sheppard, and Cheraskin.