High-precision time synchronization for remote clocks plays an important role in fundamental science and real-life applications. However, the current time synchronization techniques have been shown to be vulnerable to sophisticated adversaries. There is a compelling need for fundamentally new methods to distribute high-precision time information securely. Here we propose a satellite-based quantum-secure time transfer (QSTT) scheme based on two-way quantum key distribution (QKD) in free-space, and experimentally verify the key technologies of the scheme via the Micius quantum satellite. In QSTT, a quantum signal (e.g., single photon) is used as the carrier for both the time transfer and the secret-key generation, offering quantum-enhanced security for transferring time signal and time information. We perform a satellite-to-ground time synchronization using single-photon-level signals and achieve a quantum bit error rate of less than 1%, a time data rate of 9 kHz and a time-transfer precision of 30 ps. These results offer possibilities towards an enhanced infrastructure of time-transfer network, whose security stems from quantum physics.