MOTIVATION: Genetic perturbations (e.g. knockouts, variants) have laid the foundation for our understanding of many diseases, implicating pathogenic mechanisms and indicating therapeutic targets. However, experimental assays are fundamentally limited by the number of measurable perturbations. Computational methods can fill this gap by predicting perturbation effects under novel conditions, but accurately predicting the transcriptional responses of cells to unseen perturbations remains a significant challenge. RESULTS: We address this by developing a novel attention-based neural network, AttentionPert, which accurately predicts gene expression under multiplexed perturbations and generalizes to unseen conditions. AttentionPert integrates global and local effects in a multi-scale model, representing both the nonuniform system-wide impact of the genetic perturbation and the localized disturbance in a network of gene-gene similarities, enhancing its ability to predict nuanced transcriptional responses to both single and multi-gene perturbations. In comprehensive experiments, AttentionPert demonstrates superior performance across multiple datasets outperforming the state-of-the-art method in predicting differential gene expressions and revealing novel gene regulations. AttentionPert marks a significant improvement over current methods, particularly in handling the diversity of gene perturbations and in predicting out-of-distribution scenarios. AVAILABILITY AND IMPLEMENTATION: Code is available at https://github.com/BaiDing1234/AttentionPert.