Image-based space target detection has become one of the crucial requirements to ensure the safety of in-orbit satellites. Existing anchor-free target detection algorithms based on deep learning have achieved outstanding results. However, their detection heads have a simple structure, resulting in insufficient representation ability. To overcome this challenge, we propose a space target detection algorithm based on attention mechanism and dynamic activation. Based on the anchor-free target detection algorithm's general network structure, the channel and spatial aware-based residual attention module is employed in the detection head to improve the network's feature representation ability. Meanwhile, the channel aware-based dynamic activation module is connected in series with the detection head to enhance the network's performance in a specific space target detection task. The experimental findings on the SPARK space target detection dataset demonstrate that the proposed algorithm achieves an AP@IoU=0.50:0.95 of 77.1%, and its detection performance is substantially better than the mainstream algorithms such as Faster R-CNN, YOLOv3, and FCOS. Additionally, to further enhance the detection ability for small targets, the dynamic label assignment approach is adopted in the training process.