We demonstrated a CNT synaptic transistor by integrating 6,6-phenyl-C61 butyric acid methyl ester(PCBM) molecules as charge storage molecules in a polyimide(PI) dielectric layer with carbon nanotubes(CNTs) for the transistor channel. Specifically, we fabricated and compared three different kinds of CNT-based synaptic transistors: a control device with Al2O3/PI, a single PCBM device with Al2O3/PI:PCBM(0.1 wt%), and a double PCBM device with Al2O3/PI:PCBM(0.1 wt%)/PI:PCBM(0.05 wt%). Statistically, essential device parameters such as Off and On currents, On/Off ratio, device yield, and longterm retention stability for the three kinds of transistor devices were extracted and compared. Notably, the double PCBM device exhibited the most excellent memory transistor behavior. Pulse response properties with postsynaptic dynamic current were also evaluated. Among all of the testing devices, double PCBM device consumed such low power for stand-by and its peak current ratio was so large that the postsynaptic current was also reliably and repeatedly generated. Postsynaptic hole currents through the CNT channel can be generated by electrons trapped in the PCBM molecules and last for a relatively short time(~ hundreds of msec). Under one certain testing configuration, the electrons trapped in the PCBM can also be preserved in a nonvolatile manner for a long-term period. Its integrated platform with extremely low stand-by power should pave a promising road toward next-generation neuromorphic systems, which would emulate the brain power of 20W.