Background and Purpose: The aim of this paper is to evaluate public acceptance toward Islamic banking system in Malaysia by using the market structure analysis as proposed in industrial organizational studies. The structural approach framework was used to evaluate the nature and changes of market concentration in the Malaysian Islamic and conventional deposit markets.   Methodology: The well-known market concentration measure, namely concentration ratio (CR) is calculated to study the changes in saving behaviour among depositors in both banking markets. The concentration ratios of deposits for both banking markets are evaluated by using the banking firms’ level data for the period 1997–2016. Pearson and Spearman correlation analysis was also used to investigate the relationship between the total deposits and bank-specific variables.   Findings: It is found that interest or profit rate paid to the depositors are the factor that greatly affect the depositors’ choice of banks to save their money. Besides, experience doing businesses is more important to Islamic banks compared to conventional banks in order to attract depositors.   Contributions: The findings demonstrate that societies, especially the Islamic community, are still loyal to conventional banks, which have more experience in the banking operation. The findings of this study are expected to open the eyes of the Muslim community to use Islamic banking services, which are certainly sharia-compliance.   Keywords: Concentration ratio, deposit, dual banking, market structure, perception.   Cite as: Mohammed, N., Jauhari, A., & Mohammed, N. (2020). Customers’ deposit behaviour in dual banking industry: A market structure analysis. Journal of Nusantara Studies, 5(1), 356-377. http://dx.doi.org/10.24200/jonus.vol5iss1pp356-377