Molecule-based devices are envisioned to complement silicon devices by providing new functions or by implementing existing functions at a simpler process level and lower cost, by virtue of their self-organization capabilities. Moreover, they are not bound to von Neuman architecture and this feature may open the way to other architectural paradigms. Neuromorphic electronics is one of them. Here, a device made of molecules and nanoparticles-a nanoparticle organic memory field-effect transistor (NOMFET)-that exhibits the main behavior of a biological spiking synapse is demonstrated. Facilitating and depressing synaptic behaviors can be reproduced by the NOMFET and can be programmed. The synaptic plasticity for real-time computing is evidenced and described by a simple model. These results open the way to rate-coding utilization of the NOMFET in dynamical neuromorphic computing circuits.