The Super Tau-Charm Facility (STCF) is a future electron-positron collider proposed in China with a peak luminosity of above 0.5$times$10$^{35}$ cm$^{-2}$s$^{-1}$ and center-of-mass energy ranging from 2 to 7 GeV. An excellent particle identification (PID) capability is one of the most important requirements for the detector at the STCF. A 3$sigma$ $pi$/K separation power at the momentum of up to 2 GeV/c is required within the detector acceptance. A DIRC-like time-of-flight (DTOF) detector is proposed to meet the PID requirement for the endcap region of the STCF. The conceptual design of the DTOF detector and its geometry optimization is herein presented. The PID performance of the detector is studied using Geant4 simulation. With a proper reconstruction algorithm, an overall time resolution of ~50 ps is achieved for the detector with an optimum geometry when convoluting contributions from all other sources, including the transit time spread (TTS) of the photodetector, electronic timing accuracy, and an assumed precision (~40 ps) of the event start time. A $pi$/K separation power of better than 4$sigma$ at the momentum of 2 GeV/c is achieved over the entire sensitive area of the DTOF detector, thereby fulfilling the physics requirement of the PID detector for the experiment at the STCF.
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