In single image super-resolution (SISR), given a low-resolution (LR) image, one wishes to find a high-resolution (HR) version of it which is both accurate and photorealistic. Recently, it has been shown that there exists a fundamental tradeoff between low distortion and high perceptual quality, and the generative adversarial network (GAN) is demonstrated to approach the perception-distortion (PD) bound effectively. In this paper, we propose a novel method based on wavelet domain style transfer (WDST), which achieves a better PD tradeoff than the GAN based methods. Specifically, we propose to use 2D stationary wavelet transform (SWT) to decompose one image into low-frequency and high-frequency sub-bands. For the low-frequency sub-band, we improve its objective quality through an enhancement network. For the high-frequency sub-band, we propose to use WDST to effectively improve its perceptual quality. By feat of the perfect reconstruction property of wavelets, these sub-bands can be re-combined to obtain an image which has simultaneously high objective and perceptual quality. The numerical results on various datasets show that our method achieves the best trade-off between the distortion and perceptual quality among the existing state-of-the-art SISR methods.