A micromagnetic solver using the Finite Difference method on a Graphics Processing Unit (GPU) and its integration with the Object Oriented MicroMagnetic Framework (OOMMF) are presented. Two approaches for computing the magnetostatic field accelerated by the Fast Fourier Transform (FFT) are implemented. The first approach, referred to as the tensor approach, is based on the tensor spatial convolution to directly compute the magnetostatic field from magnetic moments. The second approach, referred to as the scalar potential approach, uses differential operator evaluation through finite differences (divergence for magnetic charge and gradient for magnetostatic field) and spatial convolution for magnetic scalar potential. Comparisons of implementation details, speed, memory consumption and accuracy are provided. The GPU implementation of OOMMF shows up to 32x GPU-CPU speed-up.