This thesis presents the application of graphics processing unit (GPU) based parallel computing technique to speed up electromagnetic transients (EMT) simulation of large power systems. GPUs support extra computing capability to handle gaming and animation related applications in the desktop computers. GPUs can be used for general-purpose computations, such as EMT simulation. Traditionally, EMT simulation tools are implemented on the CPUs, where simulation is performed in a sequential manner. Hence, with the increase in network size, there is a drastic increase in simulation times. This research shows that the use of GPU computing considerably reduces the total simulation time. This thesis proposes parallelized algorithm for EMT simulations on the GPU, and demonstrates the algorithm by simulating large power systems. Total computation times for GPU computing, using 'compute unified device architecture' (CUDA)-based C programming are compared with the total computation times for the sequential implementations on the CPU using ANSI-C programming for systems of various sizes and types. Special parallel processing techniques are implemented to model various power system components such as transmission lines, generators, etc. An advanced technique to implement parallel matrix-vector multiplication on the GPU is implemented, which shows a significant performance gain in the simulation. A sparsity-based technique for the inverse admittance matrix is implemented in this simulation process to ignore the multiplications involving zeros. A typical power electronic subsystem is also implemented in this simulation process, which had not been implemented in the literature so far for the GPU platforms. GPU computing-based simulation of large power networks with many power electronic subsystems has shown a massive performance gain compared to conventional sequential simulations with and without the sparsity technique. Finally, in this research work, the effect of granularity on the speedup of simulation was investigated. Granularity is defined as the ratio of the number of transmission lines used to interconnect various subsystems to the total size of the network. It should be noted that dividing a network into smaller subsystems requires additional transmission lines. Simulation results show that there is a negative impact on the overall performance gain of simulation with the use of excessive transmission lines in the test systems.