Lakoff and Johnson (1980) gave a cognitive point of view to metaphor study explaining that metaphor is not a mere literary stylistic device, rather a tool for conceptualization. According to this view, metaphors are conceptualized in man's mind with regard to source domain and target domain in different types of context. This study is an attempt to investigate the conceptual mapping between the metaphors in Source Language (SL) and Target Language (TL) and explain how the conceptual shift occurs between the domains. In order to do so, the metaphors in the poem "Le Bateau Ivre" by Arthur Rimbaud (1854-1891) and their translations in Turkish by Sabahattin Eyuboglu (1908-1973) are investigated within the framework of Mandelblit's (1995) Cognitive Translation Hypothesis in which the translations of the metaphors are evaluated from a cognitive perspective. A schema added by Al-Hasnawi (2007) to this hypothesis is also included in the analysis of the present study. The conclusion aimed at by the researcher is to turn focus to metaphor as a conceptualized cognitive figure in translation and to unearth the dimensions of analysis, comprehension and interpretation of metaphor in source and target language with a cognitive perspective.