In this paper we propose ExcitGlow, a vocoder that incorporates the source-filter model of voice production theory into a flow-based deep generative model. By targeting the distribution of the excitation signal instead of the speech waveform itself, we significantly reduce the size of the flow-based generative model. To further reduce the number of parameters, we apply a parameter sharing technique in which a single affine coupling layer is used for several flow layers. To avoid quality degradation, we also introduce a closed-loop training framework to optimize the flow model for both the speech and excitation signal generation processes. Specifically, we choose negative log-likelihood (NLL) loss for the excitation signal and multi-resolution spectral distance for the speech signal. As a result, we are able to reduce the model size from 87.73M to 15.60M parameters while maintaining the perceptual quality of synthesized speech.