  We have developed a gravity solver based on combining the well developed
Particle-Mesh (PM) method and TREE methods. It is designed for and has been
implemented on parallel computer architectures. The new code can deal with tens
of millions of particles on current computers, with the calculation done on a
parallel supercomputer or a group of workstations. Typically, the spatial
resolution is enhanced by more than a factor of 20 over the pure PM code with
mass resolution retained at nearly the PM level. This code runs much faster
than a pure TREE code with the same number of particles and maintains almost
the same resolution in high density regions. Multiple time step integration has
also been implemented with the code, with second order time accuracy. The
performance of the code has been checked in several kinds of parallel computer
configuration, including IBM SP1, SGI Challenge and a group of workstations,
with the speedup of the parallel code on a 32 processor IBM SP2 supercomputer
nearly linear (efficiency $\approx 80\%$) in the number of processors. The
computation/communication ratio is also very high ($\sim 50$), which means the
code spends $95\%$ of its CPU time in computation.
