As the tidal current industry grows, power extraction from tidal sites has received widespread attention. In this paper, a blade element actuator disk model that is coupled with the blade element method and a three-dimensional Navier–Stokes code is developed to analyse the relationship between power extraction and the layout of turbine arrays. First, a numerical model is constructed to simulate an isolated turbine and the model is validated using experimental data. Then, using this validated model, the power extraction of horizontal axis tidal current turbines using different tidal turbine arrays and rotation directions is predicted. The results of this study demonstrate that staggered grid array turbines can absorb more power from tidal flows than can rectilinear grid array turbines and that staggered grid array turbines are less affected by the rotation of upstream turbines. In addition, for staggered gird arrays, the relationships between power coefficients, lateral distance and longitudinal distance are discussed. The appropriate lateral distance is approximately 2.5 turbine diameters, whereas for the longitudinal distance, the largest value possible should be used. The relative power coefficient can achieve 3.74 when the longitudinal distance is 6 times the turbine diameter. To further increase the power extraction, this study suggests an improved staggered grid array layout. The relative power coefficient of the improved four-row turbine arrays is approximately 3–4% higher than that of the original arrays and will increase as the distance between the second-row and third-row increases. Considering only the first two rows of turbines, the total power extraction can be 11% higher than for an equivalent number of isolated turbines.