In the paper, a CFD method that employs the flux reconstruction (FR) method and the actuator line method (ALM) is proposed, to develop a novel numerical framework to improve the efficiency and accuracy of turbulent wake predictions of horizontal axis wind turbines (HAWT). The PyFR solver, which is an open-source program that uses the FR method is applied. The ALM is for the first time implemented in the FR solver to simulate HAWTs. To increase the fidelity of the wake prediction, the nacelle and tower of the HAWT are also modeled, and the proposed numerical simulation method is named as AL-PyFR(N&T) model. The NTNU “Blind Test 1” wind turbine is used to validate the proposed model. First, the mesh and time step dependence of the AL-PyFR(N&T) model are verified. Second, the accuracy of the proposed model is verified by comparing the velocity deficits and turbulent kinetic energy results at different downstream locations with the measured values and the results from other CFD studies. By comparison of the results with and without the effect of the nacelle and tower, it is found that tower wake plays a significant role in wake asymmetry. Crucially, the AL-PyFR(N&T) model demonstrates a capacity for accurate wake predictions with fewer mesh requirements compared to conventional CFD models. This efficiency marks a significant advancement for high-fidelity numerical simulations of offshore wind farms.