The objective of this study is to improve the time resolution value of a coincidence spectrometer used in a time-of-flight-positron emission tomography (TOF-PET) system. This spectrometer is used in medical imaging systems. The coincidence spectrometer is manufactured by using a BC420-type plastic scintillator and R1828-01-type photomultiplier tube, and the time resolution value of the manufactured spectrometer is determined. The accuracy of the experimental results is determined using the FLUKA Monte Carlo simulation program. Detectors are first manufactured in this program. Experimental and simulation results are compared and are found to be in good agreement. Optimal positions of the detectors are investigated to improve the coincidence time resolution of the spectrometer. Time resolution improvement of the optimal detector positions enables higher time-of-flight (TOF) gain and spatial resolution, leading to better image quality, reduction in patient doses and detection of small lesions.