Mobile crowd computing (MCC) that utilizes public-owned (crowd’s) smart mobile devices (SMDs) collectively can give adequate computing power without any additional financial and ecological cost. However, the major challenge is to cope with the mobility (or availability) issue of SMDs. User’s unpredicted mobility makes the SMDs really unstable resources. Selecting such erratic resources for job schedule would result in frequent job offloading and, in the worst case, job loss, which would affect the overall performance and the quality of service of MCC. In a Local MCC, generally, a set of users are available for a certain period regularly. Based on this information, the chances of a user being available for a certain duration from a given point of time can be predicted. In this paper, we provide an effective model to predict the availability of the users (i.e., their SMDs) in such an MCC environment. We argue that before submitting a job to an SMD, the stability of it is to be assessed for the duration of execution of the job to be assigned. If the predicted availability period is greater than the job size, then only the job should be assigned to the SMD. An accurate prediction will minimize the unnecessary job offloading or job loss due to the early departure of the designated SMD. We propose an advanced convolutional feature extraction mechanism that is applied to LSTM and GRU-based time-series prediction models for predicting SMD availability. To collect user mobility data, we considered a research lab scenario, where real mobility traces were recorded with respect to a Wi-Fi access point. We compared the prediction performances of convolutional LSTM and GRU with the basic LSTM and GRU and ARIMA in terms of MAE, RMSE, R2, accuracy, and perplexity. In all the measurements, the proposed convolutional LSTM exhibited considerably better prediction performance.