In the pebble-bed high-temperature reactor under construction in China, called the HTR-PM, the spherical fuel elements continuously flow downward in the cylindrical core. The burnup of each pebble is checked at the core outlet and, according to the achieved burnup level, the pebble might be disposed or reinserted into the upper section of the core. Upon reinsertion, each pebble is radially distributed in a random manner and, according to its downward path, faces different burnup conditions. Hence, the number of passes necessary to achieve the average discharge burnup of 90 MWd/kgU may vary. Discrete element method (DEM) simulations have been carried out to achieve a clear understanding of the movement of the 420000 fuel pebbles in the HTR-PM core. At the same time, neutronics properties have been investigated for a single pebble and for the full core with the Serpent 2 Monte Carlo code. As a result, one-group microscopic cross sections (XS) have been parametrized at the core level. The pebble movement has been loosely coupled with the depletion of a single pebble in a dedicated burnup script called moving pebble burnup (MPB), developed in MATLAB. 3000 single pebble burnup histories were simulated to obtain sufficient statistics and an insight into the HTR-PM burnup process. The decrease of the average burnup gained per single pass implies that a misshandling of recirculated fuel elements is unlikely to lead to an excess of the maximum allowed burnup of 100 MWd/kgU. The core demonstrates a self-compensation effect of burnup, meaning that it always compensates burnup under- or over-runs in the successive passes. In addition, gamma detection of Cs-137 has been studied as a practical method for monitoring the burnup of the discharged pebbles, turning out to be an applicable measurement technique. Finally, it is possible to conclude that the fuel cycle of the HTR-PM, as it has been laid out, is well designed and feasible.