We have recently shown that mixing nanoparticles (NPs) and molecules to implement computation and memory in a single synapse-like device is a powerful approach towards neuro-inspired computing [7]. The nanoparticle organic memory field-effect transistor (NOMFET), which we have demonstrated, can be programmed to work as a facilitating or depressing synapse; it exhibits short-term plasticity (STP) for dynamical processing of spikes. This behavior was obtained by virtue of the combination of two properties of the NOMFET: the transconductance gain of the transistor and the memory effect due to charges stored in the NPs. The NPs are used as nanoscale capacitance to store the electrical charges and they are embedded into an organic semiconductor (pentacene). Thus, the transconductance of the transistor can be dynamically tuned by the amount of charges in the NPs. This behavior was used here to implement the synaptic weight Wij with a possible dynamic working, a mandatory condition to obtain the training/learning capabilities of a spiking neural network. These results pave the way to the utilization of the NOMFET in neuromorphic computing circuits.