To better care for the elderly and disabled, it is essential for service robots to have an effective fusion method of object detection and grasp estimation. However, limited research has been observed on the combination of object detection and grasp estimation. To overcome this technical difficulty, a novel integrated method of detection-grasping for specific object based on the box coordinate matching is proposed in this paper. Firstly, the SOLOv2 instance segmentation model is improved by adding channel attention module (CAM) and spatial attention module (SAM). Then, the atrous spatial pyramid pooling (ASPP) and CAM are added to the generative residual convolutional neural network (GR-CNN) model to optimize grasp estimation. Furthermore, a detection-grasping integrated algorithm based on box coordinate matching (DG-BCM) is proposed to obtain the fusion model of object detection and grasp estimation. For verification, experiments on object detection and grasp estimation are conducted separately to verify the superiority of improved models. Additionally, grasping tasks for several specific objects are implemented on a simulation platform, demonstrating the feasibility and effectiveness of DG-BCM algorithm proposed in this paper.