This paper presents MinSpeech, a speech corpus of Southern Min (also known as Hokkien), to propel research in dialect speech recognition. Despite the linguistic and cultural importance of Southern Min, there is still a notable scarcity of publicly accessible speech corpus for this dialect. MinSpeech provides 2237 hours of unlabeled audio and 1778 hours of labeled audio, sourced diversely and encompassing various contexts. Mandarin text is employed as labels to enable cross-linguistic alignment and transformation. Using this corpus, we have developed baseline systems, including supervised models (Kaldi Chain and Conformer) and two self-supervised models (Wav2vec 2.0 and HuBERT). These systems were assessed on an automatic speech recognition (ASR) task to the Southern Min dialect. Experiments illustrate that the corpus offers practical assistance and resources for speech processing of this dialect. MinSpeech dataset is available at https://minspeech.github.io/.