The ability of scale-equivariance processing blocks plays a central role in arbitrary-scale image super-resolution tasks. Inspired by this crucial observation, this work proposes two novel scale-equivariant modules within a transformer-style framework to enhance arbitrary-scale image super-resolution (ASISR) performance, especially in high upsampling rate image extrapolation. In the feature extraction phase, we design a plug-in module called Adaptive Feature Extractor, which injects explicit scale information in frequency-expanded encoding, thus achieving scale-adaption in representation learning. In the upsampling phase, a learnable Neural Kriging upsampling operator is introduced, which simultaneously encodes both relative distance (i.e., scale-aware) information as well as feature similarity (i.e., with priori learned from training data) in a bilateral manner, providing scale-encoded spatial feature fusion. The above operators are easily plugged into multiple stages of a SR network, and a recent emerging pre-training strategy is also adopted to impulse the model’s performance further. Extensive experimental results have demonstrated the outstanding scale-equivariance capability offered by the proposed operators and our learning framework, with much better results than previous SOTAs at arbitrary scales for SR. Our code is available at https://github.com/neuralchen/EQSR.