Abstract: Accurate multivariate load forecasting is crucial for energy systems' safe and stable operation and for optimizing control and scheduling processes. Aiming at the park-level integrated energy system (PIES) characteristics, such as solid stochasticity, large uncertainty, and multiple energy sources coupling. This paper proposes a multivariate load forecasting model for the PIES based on the combination of gated recurrent unit (GRU), residual connectivity network, and multi-task learning (MTL). Firstly, a comprehensive correlation analysis method is constructed to analyze the correlation between different loads and between different loads and meteorological factors, thereby prioritizing the influencing factors. Secondly, the GRU network mines the temporal characteristics of multiple load data. In particular, the performance of the deep network is improved by residual connection (RC). Then, a hard parameter-sharing mechanism is adopted in MTL to extract the coupling information between multivariate loads. Finally, multi-task loss function optimization is used to balance multi-task training and enhance the overall performance of the prediction model. The case study analysis demonstrates that the GRU-RC-MTL model optimized by the proposed loss function shows superior predictive performance compared with other models. This validates the model's effectiveness and provides more precise multivariate load forecasting information for optimal dispatch and energy management in PIES.