A simplified digital positron lifetime spectrometer is presented and tested. This system is only composed of two scintillation detectors, a time delayer and a digital oscilloscope. Both online and offline analysis of the detector signals can be optionally chosen to construct positron lifetime spectrum by histogramming the time difference between the positron birth signal of 1.27MeV γ-ray and one positron annihilation signal of 0.511MeV γ-rays. Several pulse discrimination methods and timing numerical algorithms are proposed and well applied to perform pulse energy discrimination and digital constant fraction timing (DCFT). A combination discrimination of pulse amplitude, pulse risetime and ratio of pulse area to pulse amplitude with DCFT is found able to achieve the best time resolution of 208ps full-width at half-maximum (FWHM), which is much better over the analog spectrometer using the same detectors. This newly developed apparatus except for having better performance is particularly easy to be constructed and implemented.