Sequential recommendation models have predominantly relied on self-attention mechanisms in recent years. However, beyond self-attention, other deep neural architectures such as convolutional neural networks (CNNs) offer promising alternatives for capturing sequential patterns. In this paper, we explore the CNN-based architecture and propose Local-aware Convolutional Modulation for Short-Term Sequential Recommendation (LCMRec). Like other convolutional neural network-based models, LCMRec benefits from strong local modelling capabilities through its convolutional architecture. By introducing the multi-head convolutional modulation (MHCM) unit, which applies convolutions with varying kernel sizes across multiple heads locally, LCMRec dynamically captures short-term dependencies at multiple scales and keeps a linear computational complexity. In experiments, LCMRec outperforms baseline models, demonstrating the efficacy of the convolutional architecture and validating the effectiveness of our approach in balancing multi-scale dependency modelling with computational efficiency.