Lead-cooled Fast Reactors (LFRs) are being deeply studied within the Generation IV International Forum (GIF) framework because of their features which well suit nuclear sustainability and safety. Different design configurations have been considered, each of them requiring different modelling approaches for the study of the reactor dynamics and in particular of the most critical transients in terms of safety and control. In this work a linearized one-dimensional model of a lead-cooled fast reactor is presented assuming as reference design for the primary loop the European Lead SYstem (ELSY) reactor. Differently from the ELSY reference option, a supercritical water steam cycle is considered as secondary loop, which represents an attractive option for future developments of ELSY design. In order to properly describe the heat transfer in supercritical water, different correlations (available in open literature) have been analyzed and compared. The present model implements mass and energy equations, referred to a single-channel thermal-hydraulic analysis both for primary and secondary reactor system, handled in the frequency domain according to the theory of linear systems. The adopted transfer function approach simplifies the study of the reactor stability, and permitted to solve analytically in time the governing equations by means of Laplace transform method. Limitation of computer cost is a further benefit. The reactor dynamics has been characterized by simulating significant operational transients due to disturbances of input variables. In particular, system responses to perturbations of reactor power, feedwater temperature and mass flow rate, are discussed. Drawbacks due to the linearization and to the appearance of non-minimum phase effects related to the secondary loop modelling are pointed out also in the view of future development of a reactor control strategy. A discussion on the non-minimum phase source is also presented.