Melodic similarity is an important task in the Music Information Retrieval (MIR) domain, with promising applications including query by example, music recommendation and visualisation. Most current approaches compute the similarity between two melodic sequences by comparing their local features (distance between pitches, intervals, etc.) or by comparing the sequences after aligning them. In order to find a better feature representing global characteristics of a melody, we propose to represent the melodic sequence of each musical piece by the parameters of a generative Recurrent Neural Network (RNN) trained on its sequence. Because the trained RNN can generate the identical melodic sequence of each piece, we can expect that the RNN parameters contain the temporal information within the melody. In our experiment, we first train an RNN on all melodic sequences, and then use it as an initialisation to train an individual RNN on each melodic sequence. The similarity between two melodies is computed by using the distance between their individual RNN parameters. Experimental results showed that the proposed RNN-based similarity outperformed the baseline similarity obtained by directly comparing melodic sequences.