We describe a parallel version of our tree-code for the simulation of self-gravitating systems in Astrophysics. It is based on a dynamic and adaptive method for the domain decomposition, which exploits the hierarchical data arrangement used by the tree-code. It shows low computational costs for the parallelization overhead - less than 4% of the total CPU-time in the tests done - because the domain decomposition is performed ``on the fly'' during the tree-construction and the portion of the tree that is local to each processor ``enriches'' itself of remote data only when they are actually needed. The performance of an implementation of the parallel code on a Cray T3E is presented and discussed. They exhibit a very good behaviour of the speed...