Spike-timing-dependent plasticity (STDP) is a fundamental learning rule observed in biological synapses that is desirable to replicate in neuromorphic electronic systems. Nanocrystalline-silicon thin film transistors (TFTs) and memristors can be fabricated at low temperatures, and are suitable for use in such systems because of their potential for high density, 3-D integration. In this paper, a compact and robust learning circuit that implements STDP using biologically realistic nonmodulated rectangular voltage pulses is demonstrated. This is accomplished through the use of a novel nanoparticle memory-TFT with short retention time at the output of the neuron circuit that drives memristive synapses. Similarities to biological measurements are examined with single and repeating spike pairs or different timing intervals and frequencies, as well as with spike triplets.