With significant expansion in wind farm capacity, wake disturbances from upstream wind turbines have emerged as a detrimental factor, adversely affecting the generated power of downstream units. However, the conventional power prediction models usually neglect the wake effect between adjacent wind turbines. To bridge this gap, this paper proposes a novel power prediction model that considers the wake effect and its boundary layer compensation, to enable joint spatial and temporal wind power prediction for wind farms. Firstly, a two-dimensional convolutional neural network is adopted to extract the key features and reconstruct wind power prediction data. Secondly, utilizing historical data, a long short-term memory algorithm is employed to investigate the correlation between elemental characteristics and wind data. Subsequently, a 3D-Gaussian Frandsen wake model that accounts for the wake effect and boundary layer compensation in wind farms is developed to precisely cal-culate the spatial wind speed distributions. Consequently, these distributions allow the power outputs of wind tur-bines in wind farms to be estimated more accurately via the rotor equivalent wind speed. Finally, several case studies are conducted to validate the effectiveness of the proposed method. The results demonstrate that the suggested approach yields favorable outcomes in predicting both wind speed and wind power.