Aims. We determine the central mass distribution of galaxy cluster RX J1347−1145 using strong gravitational lensing. Methods. High-resolution HST/ACS images of the galaxy cluster RX J1347−1145 have enabled us to identify several new multipleimage candidates in the cluster, including a 5-image system with a central image. The multiple-images allow us to construct an accurate 2-dimensional mass map of the central part of the cluster. The modelling of the cluster mass includes the most prominent cluster galaxies modelled as truncated isothermal spheres and a smooth halo component that is described with 2 parametric profiles. The mass reconstruction is done using a Markov chain Monte Carlo method that provides us with a total projected mass density, as well as with estimates for the parameters of interest and their respective errors. Results. Inside the Einstein radius of the cluster (∼35 , or ∼200 kpc, for a source at redshift 1.8), we obtain a total mass of (2.6 ± 0.1) × 10 14 M . The mass profile of the cluster is well-fitted by both a Navarro, Frenk, and White profile with a moderate concentration of c = 5.3 −0.1 Mpc, and a non-singular isothermal sphere with velocity dispersion σ = 1949 ± 40 km s −1 and a core radius of r c = 20 ± 2 . The mass profile agrees with previous mass estimates based on the X-ray emission from the hot intra-cluster gas, although the X-ray mass estimates are systematically lower than what we obtain with gravitational lensing.