In the realm of robotic intelligence, achieving efficient and precise RGB-D semantic segmentation is a key cornerstone. State-of-the-art multimodal semantic segmentation methods, primarily rooted in symmetrical skeleton networks, find it challenging to harmonize computational efficiency and precision. In this work, we propose AsymFormer, a novel network for real-time RGB-D semantic segmentation, which targets the minimization of superfluous parameters by optimizing the distribution of computational resources and introduces an asymmetrical backbone to allow for the effective fusion of multimodal features. Furthermore, we explore techniques to bolster network accuracy by redefining feature selection and extracting multi-modal self-similarity features without a substantial increase in the parameter count, thereby ensuring real-time execution on robotic platforms. Additionally, a Local Attention-Guided Feature Selection (LAFS) module is used to selectively fuse features from different modalities by leveraging their dependencies. Subsequently, a Cross-Modal Attention-Guided Feature Correlation Embedding (CMA) module is introduced to further extract cross-modal representations. This method is evaluated on NYUv2 and SUNRGBD datasets, with AsymFormer demonstrating competitive results with 52.0% mIoU on NYUv2 and 49.1% mIoU on SUNRGBD. Notably, AsymFormer achieves an inference speed of 65 FPS and after implementing mixed precision quantization, it attains an impressive inference speed of 79 FPS on RTX3090. This significantly outperforms existing multi-modal methods, thereby demonstrating that AsymFormer can strike a balance between high accuracy and efficiency for RGB-D semantic segmentation.