Scene text recognition (STR) from high-resolution (HR) images has been significantly successful, however text reading on low-resolution (LR) images is still challenging due to insufficient visual information. Therefore, recently many scene text image super-resolution (STISR) models have been proposed to generate super-resolution (SR) images for the LR ones, then STR is done on the SR images, which thus boosts recognition performance. Nevertheless, these methods have two major weaknesses. On the one hand, STISR approaches may generate imperfect or even erroneous SR images, which mislead the subsequent recognition of STR models. On the other hand, as the STISR and STR models are jointly optimized, to pursue high recognition accuracy, the fidelity of SR images may be spoiled. As a result, neither the recognition performance nor the fidelity of STISR models are desirable. Then, can we achieve both high recognition performance and good fidelity? To this end, in this paper we propose a novel method called IMAGE (the abbreviation of Iterative MutuAl GuidancE) to effectively recognize and recover LR scene text images simultaneously. Concretely, IMAGE consists of a specialized STR model for recognition and a tailored STISR model to recover LR images, which are optimized separately. And we develop an iterative mutual guidance mechanism, with which the STR model provides high-level semantic information as clue to the STISR model for better super-resolution, meanwhile the STISR model offers essential low-level pixel clue to the STR model for more accurate recognition. Extensive experiments on two LR datasets demonstrate the superiority of our method over the existing works on both recognition performance and super-resolution fidelity.