Big data evidence is the evidence used in the trial to screen, summarize, refine, and form a conclusion on the massive data. Big data evidence is different from evidence analyzed or collected by big data technology. The latter does not pose a significant challenge to the traditional evidence rules, while the former leads to the maladjustment between big data evidence and traditional evidence rules, which leads to the triple dilemma of using big data evidence in court. The first dilemma is the inadaptability between the types of big data evidence and the types of legal evidence, which should be solved gradually through the three-step strategy in different periods. In the first stage, big data evidence should be regarded as an expert opinion. In the second stage, big data evidence should be regarded as an independent type of evidence. In the third stage, the practice of taking the type of evidence as the threshold of evidence review should be abandoned. The second dilemma is the relevance dilemma caused by reliability, which is due to the black box operation of big data and the complexity of big data technology. The simplest and direct solution is to disclose the historical accuracy of the algorithm. Among them, the main body of publishing the historical accuracy of the algorithm should be the algorithm developer (or improver), because an integral part of developing big data algorithm is to calculate (improve) the accuracy of the algorithm in progress. At the same time, in order to ensure the credibility of the historical accuracy published by algorithm developers (or improvers), government departments should also take the lead and rely on industry self-discipline organizations with corresponding professional talents, technical support and supervision ability to supervise the algorithm. In addition, if necessary, appraisers and expert assistants should be sought to explain, so that ordinary people can understand the relevance based on "data experience", so as to further judge the reliability of big data evidence. The third dilemma is the admissibility dilemma caused by the invasion of privacy and the influence of "evidence bias". This dilemma should be solved by constructing the integrated regulation path of "principle + system + technology". From the perspective of principle, the application principles of big data evidence include the principle of limited use of data, the principle of "weak consent" of data subjects and the principle of data screening. From the perspective of system, on the one hand, a big data technology risk assessment system should be built to assess the risk level of the application of big data technology. On the other hand, the review mechanism for the application of big data technology should be introduced, including the review of big data regulators and the review of judicial organs. From a technical point of view, the privacy protection mechanism through more advanced technologies such as "data desensitization" should be tried. In addition, the resolution of the third dilemma of big data evidence also needs the enhancement of adversary of litigation by improving the evidence discovery system and other methods.