The visual preference of users for products has been largely ignored by the existing product search methods. In this work, we propose a multi-modal personalized product search method, which aims to search products which not only are relevant to the submitted textual query, but also match the user preferences from both textual and visual modalities. To achieve the goal, we first leverage the also_view and buy_after_viewing products to construct the visual and textual latent spaces, which are expected to preserve the visual similarity and semantic similarity of products, respectively. We then propose a translation-based search model (TranSearch ) to 1) learn a multi-modal latent space based on the pre-trained visual and textual latent spaces; and 2) map the users, queries and products into this space for direct matching. The TranSearch model is trained based on a comparative learning strategy, such that the multi-modal latent space is oriented to personalized ranking in the training stage. Experiments have been conducted on real-world datasets to validate the effectiveness of our method. The results demonstrate that our method outperforms the state-of-the-art method by a large margin.