In big cities, there are plenty of parking spaces, but we often find nowhere to park. For example, New York has 1.4 million cars and 4.4 million on-street parking spaces, but it is still not easy to find a parking place near our destination, especially during peak hours. The reason is the lack of prediction of parking behavior. If we could provide parking behavior in advance, we can ease this parking problem that affects human well-being. We observe that parking lots have periodic parking patterns, which is an important factor for parking behavior prediction. Unfortunately, existing work ignores such periodic parking patterns in parking behavior prediction, and thus incurs low accuracy. To solve this problem, we propose PewLSTM, a novel periodic weather-aware LSTM model that successfully predicts the parking behavior based on historical records, weather, environments, and weekdays. PewLSTM has been successfully integrated into a real parking space reservation system, ThsParking, which is one of the top smart parking platforms in China. Based on 452,480real parking records in 683 days from 10 parking lots, PewLSTM yields 85.3% parking prediction accuracy, which is about 20% higher than the state-of-the-art parking behavior prediction method. The code and data can be obtained fromhttps://github.com/NingxuanFeng/PewLSTM.