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Terminal airspace is the convergence area of air traffic flow, which is the bottleneck of air traffic management. With the rapid growth of air traffic volume, the impact of convective weather on flight operations is becoming more and more serious. To change the conditions and improve the utilization of terminal area airspace, a convective weather terminal area capacity (CWTAC) model is developed to quantify the effect of convective weather on the capacity of the terminal area in this paper. The airspace of the terminal area is divided into major airspace, minor airspace and no-impact airspace according to the distribution of the air traffic flow. Under convective weather, their permeabilities are calculated and used as input features, and the actual availability rate is set to label. Three machine learning algorithms, support vector regression (SVR), random forest (RF), and artificial neural network (ANN), are used to predict the availability rate. Then, the terminal airspace capacity under convective weather can be calculated. The historical operation data of the Guangzhou terminal area and the Wuhan terminal area are taken to test machine learning algorithms and verify the CWTAC model. It shows that all three machine learning algorithms are practical, and ANN is the best one based on mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The predicted capacity of the CWTAC model accords well with the actual flight number in the terminal airspace under convective weather. The reasons why they are not entirely consistent are also analyzed.