A hybrid Large Eddy Simulation / transported Probability Density Function (LES-PDF) computational model is developed to perform the numerical simulation of variable-density low Mach number turbulent reactive flows. Transport equations for mass, momentum, and scalars are solved together with an equation of state within the LES framework. Turbulence is modeled using the classical Smagorinsky closure whereas chemical reaction is first addressed thanks to a global single-step chemistry scheme. The governing equations are discretized using second order accuracy spatial and temporal approximations applied to uniform Cartesian meshes within a finite volume framework. The effects of subgrid scale (SGS) turbulence on the combustion processes are accounted for by means of a Lagrangian transported PDF model which is coupled with the LES solver. The PDF model relies on the use of a Monte Carlo technique: Stochastic Differential Equations (SDE), equivalent to the Fokker- Planck equations are considered for the progress variable. LES and PDF models are solved simultaneously, exchanging information at each integration time step, the velocity field, turbulence frequency and diffusion coefficient being provided by LES, whereas the PDF model returns the filtered chemical reaction rate. Parallelization of the Lagrangian solver has been performed based on the domain decomposition strategy, the same strategy being already implemented for the eulerian LES solver. The resulting computational model is used to perform the simulation of an experimental test case consisting of a CH4-air flame established between two streams of fresh and burnt pilot gases in a constant area square cross section channel. The accuracy of the numerical solutions provided by the hybrid LESPDF approach is assessed by detailed comparisons with experimental data.