Synapse plays an important role of learning in a neural network; the learning rules which modify the synaptic strength based on the timing difference between the pre- and post-synaptic spike occurrence is termed as Spike Time Dependent Plasticity (STDP). The most commonly used rule posits weight change based on time difference between one pre- and one post spike and is hence termed doublet STDP (DSTDP). However, D-STDP could not reproduce results of many biological experiments; a triplet STDP (T-STDP) that considers triplets of spikes as the fundamental unit has been proposed recently to explain these observations. This paper describes the compact implementation of a synapse using single floating-gate (FG) transistor that can store a weight in a nonvolatile manner and demonstrate the triplet STDP (T-STDP) learning rule by modifying drain voltages according to triplets of spikes. We describe a mathematical procedure to obtain control voltages for the FG device for T-STDP and also show measurement results from a FG synapse fabricated in TSMC 0.35um CMOS process to support the theory. Possible VLSI implementation of drain voltage waveform generator circuits are also presented with simulation results.