In the context of computing 3D volumetric scores for nuclear applications, combiningMonte Carlo methods andHigh Performance Computing is key to achieve precise, computationally tractable simulations andmeet the industrial deadlines. The next-event “split exponential track-length estimator” (seTLE) is typically adapted to the estimation of a tally in a mesh. We take advantage of the computing capabilities of Graphics Processing Unit (GPU) to mitigate the CPU-intensive tasks involved in the application of the seTLE: the estimation of cross section, the sampling of many out-going pseudo-particles at collision, the ray tracing across the geometry and the accumulation of scores in volumes. We discuss the performance improvements brought by porting each of these steps to GPU. We discuss the influence of the many parameters involved, and select a working point providing the best trade-off between the acceleration factor and the GPU utilization. We show on two examples thatwe obtain an acceleration factor of 8.56 on average over the entire map for the shielding application (up to 50 behind the concrete shield), and of 6.30 on average for the criticality application (up to 16 in the burnable poison tubes), compared to standard TLE on CPU.