detection methods based on deep learning are the current research focus of computer vision. However, when detecting small objects, existing detectors often suffer from missing detection. Every pixel of hyperspectral images contain the spectral information of small object materials. Therefore, they can provide additional support for improving the detection performance on small objects. However, the adjacent bands of hyperspectral images are highly correlated. It is thus necessary to select representative bands to reduce the computational redundancy. In response, this paper proposed a hyperspectral small object detection model, which used the radial basis activation function (RBAF) to carry out spectral screening and object detection. Specifically, in view of the band redundancy of hyperspectral images, an attention mechanism based on the RBAF was designed for spectral screening. As for the high texture fuzziness and low distinguishability against the background of small objects, the resolution of input images was reconstructed first. Then, a radial basis object output network (RBOON) based on the RBAF was constructed to enhance object classification. For model simplification, spectrum screening and resolution reconstruction were integrated into an attention-based resolution reconstruction network (ABRRN). With the combination of the ABRRN and RBOON, the detection model can screen the specific spectrum and suppress false alarms and thus improve the accuracy of small object detection. Hyperspectral small object detection experiments show that the proposed method improves the two detection accuracy criteria, namely AP50 and AP50:95, by 5.4% and 0.2%, respectively, which means it is better than other methods.