We propose a dynamic network quantile regression model to investigate the quantile connectedness using a predetermined network information. We extend the existing network quantile autoregression model of Zhu et al. (2019b) by explicitly allowing the contemporaneous network effects and controlling for the common factors across quantiles. To cope with the endogeneity issue due to simultaneous network spillovers, we adopt the instrumental variable quantile regression (IVQR) estimation and derive the consistency and asymptotic normality of the IVQR estimator using the near epoch dependence property of the network process. Via Monte Carlo simulations, we confirm the satisfactory performance of the IVQR estimator across different quantiles under the different network structures. Finally, we demonstrate the usefulness of our proposed approach with an application to the dataset on the stocks traded in NYSE and NASDAQ in 2016.