Wav2vec 2.0 is an end-to-end framework of self-supervised learning for speech representation that is successful in automatic speech recognition (ASR), but most of the work has been developed with a single language: English. Therefore, it is unclear whether the self-supervised framework is effective in recognizing other languages with different writing systems, such as Korean. In this paper, we present K-Wav2Vec 2.0, which is a modified version of Wav2vec 2.0 designed for Korean ASR by exploring and optimizing various factors of the original Wav2vec 2.0. In fine-tuning, we propose a multi-task hierarchical architecture to reflect the Korean writing structure. Moreover, a joint decoder is applied to alleviate the out-of-vocabulary problem. In pre-training, we attempted the cross-lingual transfer of the pre-trained model by further pre-training the English Wav2vec 2.0 on a Korean dataset, considering limited resources. Our experimental results demonstrate that the proposed method efficiently yields robust and better performance on both Korean ASR datasets.