The problem of hallucination and omission, a long-standing problem in machine translation (MT), is more pronounced when a large language model (LLM) is used in MT because an LLM itself is susceptible to these phenomena. In this work, we mitigate the problem in an LLM-based MT model by guiding it to better word alignment. We first study the correlation between word alignment and the phenomena of hallucination and omission in MT. Then we propose to utilize word alignment as preference to optimize the LLM-based MT model. The preference data are constructed by selecting chosen and rejected translations from multiple MT tools. Subsequently, direct preference optimization is used to optimize the LLM-based model towards the preference signal. Given the absence of evaluators specifically designed for hallucination and omission in MT, we further propose selecting hard instances and utilizing GPT-4 to directly evaluate the performance of the models in mitigating these issues. We verify the rationality of these designed evaluation methods by experiments, followed by extensive results demonstrating the effectiveness of word alignment-based preference optimization to mitigate hallucination and omission.