The method of Quantitative Convergent Beam Electron Diffraction (QCBED) is used to study bonding effects in crystals. Because the accurate determination of electron charge densities requires extremely time consuming computations, the use of supercomputers is often necessary. In this article, we describe how the QCBED algorithm was modified to run on a parallel computer, an Intel Paragon. The implementation is based on the master-slave process and is explained in detail. For comparison, the program is also run on a state-of-the-art vector computer, a CRAY Y-MP. The performances of the two supercomputers are compared and results from a workstation are given as a reference. The parallel implementation is found successful. It demonstrates that parallelization of serial algorithms can be efficient when increasing accuracy and better performance are required.