Cox regression model is one of the most commonly used methods in the analysis of interval-censored failure time data.In many practical studies,the covariate effects on the failure time may not be constant over time.In recent studies,time-varying coefficients are of great interest because of their flexibility in capturing the temporal covariate effects.In this paper,we propose a Bayesian approach to dynamic Cox regression model allowing for spatial correlation with interval-censored time-to-event data.With Bayesian approach,the coefficient curve is piecewise constant and the number of jump points are estimated from data.A conditional autoregressive distribution is employed to model the spatial dependency.The posterior summaries are obtained via an efficient reversible jump Markov chain Monte Carlo algorithm.The properties of our method are illustrated by simulation studies as well as an application to the smoking cessation data in southeastern Minnesota.