This empirical paper aims at measuring customer attitudes concerning Islamic banking services and how they influence their behavioural intentions to utilise them. Islamic banking has been a fast-growing sector, offering products and services according to Sharia law. Despite being the preferred choice of banking, there is a high percentage of Muslim customers who have shifted from conventional to Islamic banking. Hence, this study aims to examine factors that influence them towards the use of Islamic banking. This is cross-sectional research, where data were collected using questionnaires. A total of 490 questionnaires were received back from adult individuals who were clients of Islamic banks. The data were analyzed using the partial least squares (PLS) method. The findings indicate that ethical organisation, Islamic values, and reputation significantly impact attitudes, whereas financial literacy has no significant impact on them. Attitude is strongly related to the behavioural intention to engage in Islamic banking services. The results also reveal that attitudes mediate the effect of Islamic values, ethical organisation, and reputation on the behavioural intention to engage in Islamic banking services, but Islamic financial literacy is not associated with customers’ behavioural mindset to enjoy such services. This study provides an example of initial empirical evidence from a Muslim majority country like Bangladesh on the relationship between Islamic values, ethical organization, Islamic financial literacy, and reputation and attitudes, which in turn lead to customers’ behavioural intentions to engage in services and products of Islamic banks.