Spatial crowdsourcing refers to a system that periodically assigns a number of location-based workers with spatial tasks nearby (e.g., taking photos or videos at some spatial locations). Previous works on the spatial crowdsourcing usually designed task assignment strategies that maximize some assignment scores, which are however only based on available workers/tasks in the system at the time point of assigning workers/tasks. These strategies may achieve local optimality, due to the neglect of future workers/tasks that may join the system. In contrast, in this paper, we aim to achieve "globally" optimal task assignments, by considering not only those present, but also future (via predictions), workers/tasks. Specifically, we formalize an important problem, namely prediction-based spatial crowdsourcing (PB-SC), which expects to obtain a "globally" optimal strategy for worker-and-task assignments, over both present and predicted task/worker locations, such that the total assignment quality score is maximized under the constraint of the traveling budget. In this paper, we design an effective grid-based prediction method to estimate spatial distributions of workers/tasks in the future, and then utilize the predicted ones in our procedure of task assignments. We prove that the PB-SC problem is NP-hard, and thus intractable. Therefore, we propose efficient approximate algorithms to tackle the PB-SC problem, including greedy and divide-and-conquer (D&C) approaches, which can efficiently assign workers to spatial tasks with high quality scores and low budget consumptions, by considering both current and future task/worker distributions. Through extensive experiments, we demonstrate the efficiency and effectiveness of our PB-SC processing approaches on real/synthetic data.