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The Fast Style Transfer methods have been recently proposed to transfer a photograph to an artistic style in real-time. This task involves controlling the stroke size in the stylized results, which remains an open challenge. In this paper, we present a stroke controllable style transfer network that can achieve continuous and spatial stroke size control. By analyzing the factors that influence the stroke size, we propose to explicitly account for the receptive field and the style image scales. We propose a StrokePyramid module to endow the network with adaptive receptive fields, and two training strategies to achieve faster convergence and augment new stroke sizes upon a trained model respectively. By combining the proposed runtime control strategies, our network can achieve continuous changes in stroke sizes and produce distinct stroke sizes in different spatial regions within the same output image.