Tsunami modelling commonly accepts the shallow-water system as governing equations where the major difficulty is the correct treatment of the non-conservative term deriving from the bathymetry variations. Finite volume method for solving the shallow-water equations with such source terms has received great attention in the two last decades. The built-in conservation property, the capacity to treat correctly discontinuities and the ability to handle complex bathymetry configurations preserving some steady-state configurations (well-balanced scheme) make the method to be very efficient. Nevertheless, it is still a challenge to build an efficient numerical scheme, with very few numerical artefacts (e.g. small numerical diffusion, correct propagation of the discontinuities, accuracy and robustess) to be used in an operational environment, and that is able to better capture the dynamics of the wet-dry interface and the physical phenomena that occur in the inundation area. In this paper, we present a new second-order finite volume code. The code is developed for the shallow-water equations with a non-conservative term based on the hydrostatic reconstruction technology to achieve a well-balanced scheme and an adequate dry/wet interface treatment. A detailed presentation of the numerical method is given. Finally, we highlight the advantages of the new numerical technique. We benchmark the numerical code against analytical and experimental results to assess the ro-bustness and the accuracy, showing good agreement. To increase the reliability of the presented code, we tested the real case tsunami propagation in a complex bathymetry, the 28 February 1969 tsunami in the Tagus estuary. The comparison between the synthetic and the recorded signal shows a good reproduction of the waveforms and travelling times.