In this paper, to help handle wind farm optimization problems, an original analytical three-dimensional wind turbine wake model is presented and validated. Compared with existing analytical wake models, the presented wake model also considers the wind variation in the height direction, which is more accurate and closer to the reality. The wake model is based on the flow flux conservation law, and it assumes that the wind deficit downstream of a wind turbine is Gaussian-shaped. The derivation process is described in detail. The wake model is validated by published wind tunnel measurement data at both horizontal and vertical sections. Detailed relative errors are analyzed: the relative errors are mostly within 5% in the horizontal profile validation and within 3% in the vertical profile validation. Based on the wake model, a series of prediction results from multiple views and at different positions are demonstrated. From the predictions, the three-dimensional wake model is effective in describing the spatial distribution of wind velocity. It makes a theoretical contribution to the single wake study, and it is also meaningful to the further study of multiple wakes. Because height is considered in the three-dimensional wake model, the model can be used to optimize wind turbine hub heights and to solve more wind farm layout optimization problems, which will further contribute to increasing the energy output and decreasing the cost of energy.