Air-writing is an emerging and promising method for contactless human-machine interaction. This paper proposes a novel air-writing framework based on a single ultra wide-band radar (UWB). The framework employs a simple data capture and a processing pipeline facilitated by deep learning approaches, where a number of data representations and models are explored. Two different data representations are proposed, two-dimensional and three-dimensional range-Doppler spectrogram. The deep learning approaches include, fully connected neural networks, convolutional neural networks, three-dimensional convolutional neural networks, and hybrid two-dimensional and three-dimensional convolutional neural networks long short-term memory recurrent neural networks. A dataset of 1,800 samples containing 10 air-written numbers is collected to train, validate, and test the performance of the proposed methods. It is shown that hybrid convolutional neural networks long short-term memory recurrent neural networks architectures can effectively predict air-written numbers with an accuracy of 98.5%. The experimental results suggest the efficacy of the proposed approaches for practical and convenient air-writing applications.