Mobile applications (apps) have grown drastically since their birth in 2008. Acquiring more app users as quickly as possible after the app is released in the app stores is one of the key rules for app developers to survive in this emerging and competitive digital market. This paper uses cumulative weekly downloading data from the US Apple App Store during a two-year period of 2015 and 2016 to study the early expansion curves and diffusion patterns of mobile apps in the app market. Downloading payment methods (free or paid to download an app) and hedonic or utilitarian value-orientated app types (games and productivity apps) are considered when we study the diffusion pattern of mobile apps. The Bass model is used as the baseline model, and the logistic model and Gompertz model are used to conduct a robustness check. Nonlinear least squares (NLS) is the measurement to obtain parameters of diffusion models. The results show that the Bass model is the best-fitting model compared with the other two models, and the diffusion pattern of mobile apps is S-shaped at the market level. The first 35 weeks are essential for the app developers to attract app users' downloads. More app data from different app stores and more diffusion models can be tested for mobile app diffusion and early expansion patterns in future research.