The mobile banking is an increasingly popular service for customers of the traditional banking industry. On the surface, China has the highest adoption rate of this new technology, yet many users do not remain active or they only use mobile banking for the simplest tasks such as checking their balance. This research was designed to uncover the reasons for these two issues by identifying the major factors influencing users' intention to continue using mobile banking (continuance intention) as well as their behavioural intention to try new mobile banking functions. To do so, an integrated model was developed on the basis of the unified theory of acceptance and use of technology model (UTAUT), task-technology fit model (TTF) and expectation confirmation model (ECM). Empirical data were collected from China's mobile banking users and the integrated model was tested using Partial Least Squares Structural Equation Modelling (PLS-SEM) approach. The results indicate that the main factors which positively influence the continuance intention include satisfaction, performance expectancy and effort expectancy. Continuance intention, in turn, influences behavioural intention to try new functionality, together with social influence, facilitating conditions and confirmation. Moreover, some mediating effects were discovered. For example, task-technology fit may indirectly affect the continuance intention through users' satisfaction. The research results have a number of theoretical contributions. Firstly, this research discovers that the impact of task-technology fit on users' continuance intention towards mobile banking is fully mediated by users' satisfaction. This enriches the extant literature that is mostly focused on the technology perceptions (e.g. performance expectancy and effort expectancy) of users. Secondly, this research identifies that satisfaction also mediates the impact of confirmation of expectations on continuance intention, also extending the literature on the continuance usage of information systems. Thirdly, this research fills the gap in extant research regarding users' intention to try new mobile banking functions, by proposing a new integrated model using constructs from UTAUT, TTF, and ECM, and demonstrating that continuance intention itself fully mediates the impact of performance expectancy and effort expectancy on behavioural intention. The new model has a high explanatory power than each individual model offers. The research results also have management implications in terms of how to improve the task-technology fit to support continuous use and extended the use of mobile banking. For instance, to improve continuance intention banks can improve satisfaction by optimising task-technology fit. This in turn will require better understanding of users' different task requirements in specific market segments. In addition, banks can also attract users' behavioural intention to try new functionality by timely updating corresponding technology and launching marketing campaigns to keep users informed of any new functions of their mobile banking application.