A moisture advection scheme is an essential module of a numerical weather/climate model representing the horizontal transport of water vapor. The Piecewise Rational Method (PRM) scalar advection scheme in the Global/Regional Assimilation and Prediction System (GRAPES) solves the moisture flux advection equation based on PRM. Computation of the scalar advection involves boundary exchange, and computation of higher bandwidth requirements is complicated and time-consuming in GRAPES. Recently, Graphics Processing Units (GPUs) have been widely used to solve scientific and engineering computing problems owing to advancements in GPU hardware and related programming models such as CUDA/OpenCL and Open Accelerator (OpenACC). Herein, we present an accelerated PRM scalar advection scheme with Message Passing Interface (MPI) and OpenACC to fully exploit GPUs’ power over a cluster with multiple Central Processing Units (CPUs) and GPUs, together with optimization of various parameters such as minimizing data transfer, memory coalescing, exposing more parallelism, and overlapping computation with data transfers. Results show that about 3.5 times speedup is obtained for the entire model running at medium resolution with double precision when comparing the scheme’s elapsed time on a node with two GPUs (NVIDIA P100) and two 16-core CPUs (Intel Gold 6142). Further, results obtained from experiments of a higher resolution model with multiple GPUs show excellent scalability.