The purpose of the relativistic heavy-ion experiment E810 at the Brookhaven National Laboratory Alternating Gradient Synchrotron(BNL AGS) is to look for indications of a phase transition from hadronic to quark matter: the Quark-Gluon Plasma(QGP). The experiment was performed using a 14.5 × A Gev/c silicon beam from the BNL AGS to bombard targets of Si, Cu, Sn, Au, and Pb. The experimental apparatus used in the June 1989 run were the BNL Multi-Particle Spectrometer(MPS), the Time Projection Chamber(TPC) system, and the Time-of-Flight(TOF) hodoscope. With a 15m flight path, to separate π\sp− from p up to 5-6 Gev/c and π\sp− from k\sp− up to 2.5-3 Gev/c, we require that the Root-Mean-Square(RMS) time resolution of the TOF hodoscope be about 150 picoseconds. From the analysis of the TOF beta distribution of fast π\sp−, a RMS time resolution range of 150-160 ps can be achieved after the time-walk correction.