The aim of this thesis is to present a new Monte-Carlo simulation of double parton scattering (DPS) named dShower. DPS is the process where two separate parton-parton interactions happen in a single proton-proton collision and constitutes an important background signal to numerous processes of interest such as diboson pair production or four-jet production. An accurate modelling of DPS requires to account for the correlations between the partons belonging to the same proton. In particular, it is necessary to take into account the fact that two partons may have a common origin in a single parton due to the so-called "one-to-two" perturbative splitting mechanism. Including this splitting effect is a cumbersome task since it leads to a potential double counting with single parton scattering (SPS). Indeed, a DPS process where a one-to-two splitting happens in each proton can be seen as a loop correction to SPS. The dShower simulation introduced in this thesis allows the user to generate parton-level DPS events. The two hard scatters are sampled according to the full DPS cross section and are evolved simultaneously with a parton shower. In the algorithm, the one-to-two splitting mechanism is included in a consistent manner. DPS and SPS events can also be combined in the simulation without double counting. Some numerical results for same-sign WW and ZZ pair production are presented in the thesis.