Abstract—Fog-cloud computing is a promising platform for processing Mobile Crowdsensing (MCS) tasks that come with different requirements. A fog environment is more suitable for processing time-sensitive tasks due to its proximity to the MCS layer. On the other hand. the cloud environment provides powerful resources to handle large tasks. However, due to the heterogeneity of the computing nodes, scheduling MCS tasks in a fog-cloud environment is a challenging issue. This paper presents a non-cooperative game theoretical model for the task scheduling problem of MCS tasks in the fog-cloud environment. Then, the paper presents an improved genetic algorithm to efficiently solve the problem of task scheduling game model with main enhancements including a new strategy to generate a diverse initial population, incorporating the utility function of the game theoretical model with system fitness function, and finally, the paper introduces a new strategy for population sorting and grouping with applying adaptive crossover operator to meet the specific needs of each group. This improves the exploration of the unseen regions of the search space, as well as exploiting the already-found promising solutions, ultimately leading to a faster convergence toward the optimal solution. The experimental results demonstrate that the proposed approach has better performance in terms of reducing the makespan by 26%, decreasing the energy consumption by 32.4%, decreasing total system cost by 28%, and decreasing the degree of imbalance by 21.53% as compared with other scheduling approaches such as Discrete Non-dominated Sorting Genetic Algorithm II (DNSGA-II), Grasshopper Optimization Algorithm (GOA), Grey Wolf Optimization (GWO, Time-Cost Aware Scheduling (TCaS), Moth Flame Optimization (MFO), and Bees Life Algorithm (BLA).