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With the rising popularity of intelligent mobile devices, it is of great practical significance to develop accurate, realtime and energy-efficient image Super-Resolution (SR) inference methods. A prevailing method for improving the inference efficiency is model quantization, which allows for replacing the expensive floating-point operations with efficient fixed-point or bitwise arithmetic. To date, it is still challenging for quantized SR frameworks to deliver feasible accuracy-efficiency trade-off. Here, we propose a Fully Quantized image Super-Resolution framework (FQSR) to jointly optimize efficiency and accuracy. In particular, we target on obtaining end-to-end quantized models for all layers, especially including skip connections, which was rarely addressed in the literature. We further identify training obstacles faced by low-bit SR networks and propose two novel methods accordingly. The two difficulites are caused by 1) activation and weight distributions being vastly distinctive in different layers; 2) the inaccurate approximation of the quantization. We apply our quantization scheme on multiple mainstream super-resolution architectures, including SRResNet, SRGAN and EDSR. Experimental results show that our FQSR using low bits quantization can achieve on par performance compared with the full-precision counterparts on five benchmark datasets and surpass state-of-the-art quantized SR methods with significantly reduced computational cost and memory consumption.