Mobile crowdsensing has shown elegant capacity in data collection and has given rise to numerous applications. In the sense of coverage quality, marginal works have considered the efficient (less cost) and effective (considerable coverage) design for mobile crowdsensing networks. We investigate the optimal quality-aware coverage in mobile crowdsensing networks. The difference between ours and the conventional coverage problem is that we only select a subset of mobile users so that the coverage quality is maximized with constrained budget. To address this new problem, which is proved to be NP-hard, we first prove that the set function of coverage quality is nondecreasing submodular. By leveraging the favorable property in submodular optimization, we then propose an (1 - (1/e)) approximation algorithm with O(n ^k+2 ) time complexity, where k is an integer that is greater than or equal to 3. Finally, we conduct extensive simulations for the proposed scheme, and the results demonstrate that ours outperforms the random selection scheme and one of the state of the art in terms of total coverage quality by, at most, 2.4× and 1.5× and by, on average, 1.4× and 1.3×, respectively. Additionally, ours achieves a near-optimal solution, compared with the brute-force search results.