Existing methods often ignore the correlations between variables or fail to consider their dynamic and delayed nature, which may affect the prediction accuracy. The main goal of this study is to address the challenges in time series prediction by effectively capturing the inter-dependencies between multiple variables. We propose the LCformer model, a new framework based on the Transformer architecture that integrates the lagged correlation information of multiple variables and its own historical information. The model identifies relevant exogenous variables using an exogenous variable filter (EVF), and employs a novel additive attention embedding (AAE) layer as well as cross-attention mechanism to simulate the lagged dependencies between these exogenous variables and the target variable. Experimental evaluation shows that the LCformer model is competitive with state-of-the-art methods, confirming its ability to accurately capture complex relationships in time series data, and learning multivariate lagged correlations, which can significantly improve prediction accuracy.