The fast Hartley (FHT) transform which was first described by Ronald Bracewell can be applied to many scientific and engineering problems. We describe a way to solve the Poisson equation using the Hartley transform in this paper. We show that the Poisson equation can be solved using FH in the same way as exactly FFT does. The results of the timing test comparing the Poisson solver using FHT and that of complex FFT are also shown.