The Bengalese Finch Lonchura striata var. domestica has highly complex songs with element sequences similar in syntactic structure to that of human language. Because young learn songs by comparing their auditory memory of their father's songs to the auditory feedback of a self-generated song, it is important to understand the auditory neural representation of element sequences. We developed a spiking neural network model of the song-control nucleus HVC that changes the weight among connected neurons via spike-timing-dependent plasticity (STDP), a biologically plausible learning rule. In the model, the dynamics of neural population converged into a stable activity distribution after sufficient learning steps. The network activity differentiated element pairs included in the input sequence from those that were not. Linear input sequences had better fine response selectivity for typical pairs than random or syntax inputs. However, real HVC neurons of Bengalese Finch respond to a wider range of pair stimuli. Thus, the actual neural representation of Bengalese Finch may be more broadly distributed, possibly because of simple STDP and other additive parameters or components. From a theoretical viewpoint, one of the most reliable neural coding schemes, Cantor coding, is a distributed, sequential coding system using fractal properties. We hypothesize that Bengalese Finch learn their complex song element sequences via Cantor coding.