The 2020 Personalized Voice Trigger Challenge (PVTC2020) addresses two different research problems a unified setup: joint wake-up word detection with speaker verification on close-talking single microphone data and far-field multi-channel microphone array data. Specially, the second task poses an additional cross-channel matching challenge on top of the far-field condition. To simulate the real-life application scenario, the enrollment utterances are recorded from close-talking cell-phone only, while the test utterances are recorded from both the close-talking cell-phone and the far-field microphone arrays. This paper introduces our challenge setup and the released database as well as the evaluation metrics. In addition, we present a joint end-to-end neural network baseline system trained with the proposed database for speaker-dependent wake-up word detection. Results show that the cost calculated from the miss rate and the false alarm rate, can reach 0.37 in the close-talking single microphone task and 0.31 in the far-field microphone array task. The official website and the open-source baseline system have been released.