We present a Bayesian hierarchical model for quantitative real-time polymerase chain reaction (PCR) data, aiming at relative quantification of DNA copy number in different biological samples. The model is specified in terms of a hidden Markov model for fluorescence intensities measured at successive cycles of the polymerase chain reaction. The efficiency of the reaction is assumed to depend on the abundance of the target DNA through fluorescence intensities, and the relationship is specified based on the kinetics of the reaction. The model incorporates the intrinsic random nature of the process as well as measurement error. Taking a Bayesian inferential approach, marginal posterior distributions of the quantities of interest are estimated using Markov chain Monte Carlo. The method is applied to simulated data and an experimental data set.