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Learning-based methods have effectively promoted the community of image compression. Meanwhile, variational autoencoder (VAE) based variable-rate approaches have recently gained much attention to avoid the usage of a set of different networks for various compression rates. Despite the remarkable performance that has been achieved, these approaches would be readily corrupted once multiple compression/decompression operations are executed, resulting in the fact that image quality would be tremendously dropped and strong artifacts would appear. Thus, we try to tackle the issue of high-fidelity fine variable-rate image compression and propose the Invertible Activation Transformation (IAT) module. We implement the IAT in a mathematical invertible manner on a single rate Invertible Neural Network (INN) based model and the quality level (QLevel) would be fed into the IAT to generate scaling and bias tensors. IAT and QLevel together give the image compression model the ability of fine variable-rate control while better maintaining the image fidelity. Extensive experiments demonstrate that the single rate image compression model equipped with our IAT module has the ability to achieve variable-rate control without any compromise. And our IAT-embedded model obtains comparable rate-distortion performance with recent learning-based image compression methods. Furthermore, our method outperforms the state-of-the-art variable-rate image compression method by a large margin, especially after multiple re-encodings.