On a wind farm, the wake has an important impact on the performance of the wind turbines. For example, the wake of an upstream wind turbine affects the blade load and output power of the downstream wind turbine. In this paper, a modified actuator line model with blade tips, root loss, and an airfoil three-dimensional delayed stall was revised. This full-scale modified actuator line model with blades, nacelles, and towers, was combined with a Large Eddy Simulation, and then applied and validated based on an analysis of wind turbine wakes in wind farms. The modified actuator line model was verified using an experimental wind turbine. Subsequently, numerical simulations were conducted on two NREL 5 MW wind turbines with different staggered spacing to study the effect of the staggered spacing on the characteristics of wind turbines. The results show that the output power of the upstream turbine stabilized at 5.9 MW, and the output power of the downstream turbine increased. When the staggered spacing is R and 1.5R, both the power and thrust of the downstream turbine are severely reduced. However, the length of the peaks was significantly longer, which resulted in a long-term unstable power output. As the staggered spacing increased, the velocity in the central near wake of the downstream turbine also increased, and the recovery speed at the threshold of the wake slowed down. The modified actuator line model described herein can be used for the numerical simulation of wakes in wind farms.