The design and operation support of hadron (proton and heavy-ion) linear accelerators require substantial use of beam dynamics simulation tools. The beam dynamics code TRACK has been originally developed at Argonne National Laboratory (ANL) to fulfill the special requirements of the rare isotope accelerator (RIA) accelerator systems. From the beginning, the code has been developed to make it useful in the three stages of a linear accelerator project, namely, the design, commissioning, and operation of the machine. To realize this concept, the code has unique features such as end-to-end simulations from the ion source to the final beam destination and automatic procedures for tuning of a multiple charge state heavyion beam. The TRACK code has become a general beam dynamics code for hadron linacs and has found wide applications worldwide. Until recently, the code has remained serial except for a simple parallelization used for the simulation of multiple seeds to study the machine errors. To speed up computation, the TRACK Poisson solver has been parallelized. This paper discusses different parallel models for solving the Poisson equation with the primary goal to extend the scalability of the code onto 1024 and more processors of the new generation of supercomputers known as BlueGene (BG/L). Domain decomposition techniques have been adapted and incorporated into the parallel version of the TRACK code. To demonstrate the new capabilities of the parallelized TRACK code, the dynamics of a 45 mA proton beam represented by 108 particles has been simulated through the 325 MHz radio frequency quadrupole and initial accelerator section of the proposed FNAL proton driver. The results show the benefits and advantages of large-scale parallel computing in beam dynamics simulations.