This study propose a fully automated system for speech correction and accent reduction. Consider the application scenario that a recorded speech audio contains certain errors, e.g., inappropriate words, mispronunciations, that need to be corrected. The proposed system, named CorrectSpeech, performs the correction in three steps: recognizing the recorded speech and converting it into time-stamped symbol sequence, aligning recognized symbol sequence with target text to determine locations and types of required edit operations, and generating the corrected speech. Experiments show that the quality and naturalness of corrected speech depend on the performance of speech recognition and alignment modules, as well as the granularity level of editing operations. The proposed system is evaluated on two corpora: a manually perturbed version of VCTK and L2-ARCTIC. The results demonstrate that our system is able to correct mispronunciation and reduce accent in speech recordings. Audio samples are available online for demonstration https://daxintan-cuhk.github.io/CorrectSpeech/ .