Large Language Models (LLMs) have revolutionized text generation, making detecting machine-generated text increasingly challenging. Although past methods have achieved good performance on detecting pure machine-generated text, those detectors have poor performance on distinguishing machine-revised text (rewriting, expansion, and polishing), which can have only minor changes from its original human prompt. As the content of text may originate from human prompts, detecting machine-revised text often involves identifying distinctive machine styles, e.g., worded favored by LLMs. However, existing methods struggle to detect machine-style phrasing hidden within the content contributed by humans. We propose the "Imitate Before Detect" (ImBD) approach, which first imitates the machine-style token distribution, and then compares the distribution of the text to be tested with the machine-style distribution to determine whether the text has been machine-revised. To this end, we introduce style preference optimization (SPO), which aligns a scoring LLM model to the preference of text styles generated by machines. The aligned scoring model is then used to calculate the style-conditional probability curvature (Style-CPC), quantifying the log probability difference between the original and conditionally sampled texts for effective detection. We conduct extensive comparisons across various scenarios, encompassing text revisions by six LLMs, four distinct text domains, and three machine revision types. Compared to existing state-of-the-art methods, our method yields a 13% increase in AUC for detecting text revised by open-source LLMs, and improves performance by 5% and 19% for detecting GPT-3.5 and GPT-4o revised text, respectively. Notably, our method surpasses the commercially trained GPT-Zero with just $1,000$ samples and five minutes of SPO, demonstrating its efficiency and effectiveness.