A time domain methodology is proposed for the harmonic state estimation (HSE) in power systems based on parallel Kalman filter (PKF) algorithm implemented on a graphical processing unit (GPU). The output variable measurements to be used by the HSE are taken from the simulation of the harmonics propagation in the power system. The time domain HSE solution process is based on the application of the PKF algorithm to estimate the waveforms for nodal voltages and line currents with various sources of harmonics, time-varying harmonics and inter-harmonics. The results obtained with the PKF to solve the HSE are validated against the transient program PSCAD/EMTDC. The PKF algorithm is implemented using the Compute Unified Device Architecture (CUDA) platform and the CUDA Basic Linear Algebra Subprograms (CUBLAS) library on a NVIDIA GPU card. Case studies show the effectiveness of the PKF to solve the HSE on the GPU, the speed-up is dependent of the size and complexity of the network model.