Mobile authentication/identification has grown into a priority issue nowadays because of its existing outdated mechanisms, such as PINs or passwords. In this paper, we introduce gait recognition by using a mobile accelerometer as not only effective but also as an implicit identification model. Unlike previous works, the gait recognition only performs well with a particular mobile specification (e.g., a fixed sampling rate). Our work focuses on constructing a unique adaptive mechanism that could be independently deployed with the specification of mobile devices. To do this, the impact of the sampling rate on the preprocessing steps, such as noise elimination, data segmentation, and feature extraction, is examined in depth. Moreover, the degrees of agreement between the gait features that were extracted from two different mobiles, including both the Average Error Rate (AER) and Intra-class Correlation Coefficients (ICC), are assessed to evaluate the possibility of constructing a device-independent mechanism. We achieved the classification accuracy approximately $91.33{pm}0.67%$ for both devices, which showed that it is feasible and reliable to construct adaptive cross-device gait recognition on a mobile phone.