Physical and engineering practicalities involved in microprocessor design have resulted in flat performance growth for traditional single-core microprocessors. The urgent need for continuing increases in the performance of scientific applications requires the use of many-core processors and accelerators such as graphics processing units (GPUs). This paper discusses GPU acceleration of the multilevel summation method for computing electrostatic potentials and forces for a system of charged atoms, which is a problem of paramount importance in biomolecular modeling applications. We present and test a new GPU algorithm for the long-range part of the potentials that computes a cutoff pair potential between lattice points, essentially convolving a fixed 3-D lattice of "weights" over all sub-cubes of a much larger lattice. The implementation exploits the different memory subsystems provided on the GPU to stream optimally sized data sets through the multiprocessors. We demonstrate for the full multilevel summation calculation speedups of up to 26 using a single GPU and 46 using multiple GPUs, enabling the computation of a high-resolution map of the electrostatic potential for a system of 1.5 million atoms in under 12 seconds.