The present study introduces a stochastic Lagrangian agglomeration model to be applied within the framework of the classical Euler/Lagrange approach. The main subject of this contribution will concentrate on the modelling of the turbulent particle transport and a comprehensive modelling of particle collision and agglomeration. In the Lagrangian approach, the dynamic equation of motion for each individual particle is solved, and the properties of the particulate phase are given by the ensemble average over a large number of particles. The description of particle agglomeration in turbulent flow is governed by three consecutive and interrelated processes: The particle collisions in turbulent flow are calculated on the basis of the stochastic collision model (Sommerfeld, Int. J. Multiphase Flow 27 (2001) 1828), considering the collision efficiency due to geometrical Size difference as a function of relative Stokes number, and modelling the agglomeration efficiency determined by the sticking potential due to the van der Waals forces. To analyse the agglomeration model, a homogeneous isotropic turbulent field is considered. The particle volume fraction is chosen to be small, so that the concentration condition for dilute two-phase flow is fulfilled and the modulation of turbulence due to the particle phase may be neglected. Under different boundary conditions, such as turbulence intensity and particle relaxation times, the time-dependent change of particle size distribution and number concentration is calculated. These numerical results allow one to understand the effect of the considered parameters on the agglomeration process.