A foil-microchannel plate (MCP) detector, which uses electrostatic lenses and possesses both good position and timing resolutions, has been designed and simulated for beam diagnostics and mass measurements at the next-generation heavy-ion-beam facility HIAF in China. Characterized by low energy loss and good performances of timing and position measurements, it would be located at focal planes in fragment separator HFRS for position monitoring, beam turning, Bρ measurement, and trajectory reconstruction. Moreover, it will benefit the building-up of a magnetic-rigidity-energy-loss-time-of-flight (Bρ-∆E-TOF) method at HFRS for high-precision in-flight particle identification (PID) of radioactive isotope (RI) beams on an event-by-event basis. Most importantly, the detector can be utilized for in-ring TOF and position measurements, beam-line TOF measurements at two achromatic foci, and position measurements at a dispersive focus of HFRS, thus making it possible to use two complementary mass measurement methods (isochronous mass spectrometry (IMS) at the storage ring SRing and magnetic-rigidity-time-of-flight (Bρ-TOF) at the beam-line HFRS) in one single experimental run.