Translating poetry is a challenging task because it must take into account linguistic and cultural differences between the source language and the target languages. This paper examines John Donne's "Elegy 19: To His Mistris Going to Bed" by exploring the linguistic difficulties involved in translation, especially in grammatical categories such as word order, number, article, and preposition as well as cultural difficulties, particularly in lexis, such as culture-specific words, metaphors, and collocations. This paper suggests a suitable translation strategy to satisfy Korean readers, considering the three main translation approaches: literal translation, free translation, and an eclectic approach that connects the two extremes. Given the cultural and linguistic differences between the two languages and the idealized target readers seeking an intimate knowledge of English poetry, an eclectic translation method combining both literal and free translation seems most suitable in translating "Elegy 19" into Korean. Chang Jun Lee, translator of the target text, clearly attempts both a literal translation when dealing with the cultural aspects of words insofar as the bounds that Korean grammar allows, and a free translation with respect to grammatical categories, for the sake of the content. He thereby achieves results that allow the reader to follow the target text smoothly, though with a slightly alien impression.