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The personalized recommendation is an essential part of modern e-commerce, where user's demands are not only conditioned by their profile but also by their recent browsing behaviors as well as periodical purchases made some time ago. In this paper, we propose a novel framework named Search-based Time-Aware Recommendation (STARec), which captures the evolving demands of users over time through a unified search-based time-aware model. More concretely, we first design a search-based module to retrieve a user's relevant historical behaviors, which are then mixed up with her recent records to be fed into a time-aware sequential network for capturing her time-sensitive demands. Besides retrieving relevant information from her personal history, we also propose to search and retrieve similar user's records as an additional reference. All these sequential records are further fused to make the final recommendation. Beyond this framework, we also develop a novel label trick that uses the previous labels (i.e., user's feedbacks) as the input to better capture the user's browsing pattern. We conduct extensive experiments on three real-world commercial datasets on click-through-rate prediction tasks against state-of-the-art methods. Experimental results demonstrate the superiority and efficiency of our proposed framework and techniques. Furthermore, results of online experiments on a daily item recommendation platform of Company X show that STARec gains average performance improvement of around 6% and 1.5% in its two main item recommendation scenarios on CTR metric respectively.