Internet banking adoption is one area that has received attention from scholars. The extant studies have mainly used technology acceptance models and behavioural theories which do not account for changes in human behaviour. This study seeks to ascertain the determinants of Internet banking adoption intentions using the social cognitive theory, which accounts for changes in human behaviour. The study selected the sample from bank customers in Ghana through an intercept approach using structured questionnaires. A two stage-approach of confirmatory factor analysis and a structural equation modelling were used in analysing the data. The findings show that websites' social feature, trust, compatibility with lifestyle and online customer services have a significant effect on customers' intentions to adopt Internet banking. However, ease of use did not have a significant relationship with customers' intentions to adopt Internet banking. The significance of the study as well as recommendations for theory, practice and future studies have been discussed.