NBSymple is a numerical code which numerically integrates the equation of motions of N 'particles' interacting via Newtonian gravitation and move in an external galactic smooth field. The force evaluation on every particle is done by mean of direct summation of the contribution of all the other system's particle, avoiding truncation error. The time integration is done with second-order and sixth-order symplectic schemes. NBSymple has been parallelized twice, by mean of the Computer Unified Device Architecture to make the all-pair force evaluation as fast as possible on high-performance Graphic Processing Units NVIDIA TESLA C 1060, while the O(N) computations are distributed on various CPUs by mean of OpenMP Application Program. The code works both in single precision floating point arithmetics or in double precision. The use of single precision allows the use at best of the GPU performances but, of course, limits the precision of simulation in some critical situations. We find a good compromise in using a software reconstruction of double precision for those variables that are most critical for the overall precision of the code.