We have developed a relativistic, radiation-hydrodynamics Lagrangian code, specifically tailored to simulate the evolution of the main observables (light curve and the evolution of photospheric velocity and temperature) in core-collapse supernova (CC-SN) events. The distinctive features of the code are an accurate treatment of radiative transfer coupled to relativistic hydrodynamics, a self-consistent treatment of the evolution of the innermost ejecta taking into account the gravitational effects of the central compact remnant, and a fully implicit Lagrangian approach to the solution of the coupled nonlinear finite difference system of equations. Our aim is to use it as a numerical tool to perform calculations of a grid of models to be compared with observations of CC-SNe. In this paper, we present some testcase simulations and a comparison with observations of SN 1987A, as well as with the results obtained with other numerical codes. We also briefly discuss the influence of the main physical parameters (ejected mass, progenitor radius, explosion energy, amount of 56Ni) on the evolution of the ejecta, and the implications of our results in connection with the possibility to 'standardize' hydrogen-rich CC-SNe for using them as candles to measure cosmological distances.