Image restoration under multiple adverse weather conditions aims to remove weather-related artifacts by using the single set of network parameters. In this paper, we find that distorted images under different weather conditions contain general characteristics as well as their specific characteristics. Inspired by this observation, we design an efficient unified framework with a two-stage training strategy to explore the weather-general and weather-specific features. The first training stage aims to learn the weather-general features by taking the images under various weather conditions as the inputs and outputting the coarsely restored results. The second training stage aims to learn to adaptively expand the specific parameters for each weather type in the deep model, where requisite positions for expansion of weather-specific parameters are learned automatically. Hence, we can obtain an efficient and unified model for image restoration under multiple adverse weather conditions. Moreover, we build the first real-world benchmark dataset with multiple weather conditions to better deal with real-world weather scenarios. Experimental results show that our method achieves superior performance on all the synthetic and real-world benchmark datasets.