Depression is a global psychological disease that does serious harm to people. Traditional diagnostic method of the doctor-patient communication, is not objective and accurate enough. Thus, a more accurate and objective method for depression detection is urgently needed. Resting-state electroencephalography (EEG) can effectively reflect brain function, which have been used to study the difference of the brain between the depression patients and normal controls. In this work, the Resting-state EEG data of 27 depression patients and 28 normal controls was used in this study. We constructed the brain functional network using correlation, and extracted four linear features of EEG (activity, mobility complexity and power spectral density). We utilized a learnable weight matrix in the input layer of graph convolution neural network, creatively took the brain function network as the adjacency matrix input and the linear feature as the node feature input. We proposed our model Graph Input layer attention Convolutional Network (GICN), and it provided a good performance, showing the accuracy of 96.50% for recognition of depression and normal with 10-fold cross-validation, which indicated that our model could be used as an effective auxiliary tool for depression recognition. Besides, our method significantly outperformed other method. Additionally, the learnable weight matrix in the input layer was also used to find some edges and nodes that played an important role in depression recognition. Our findings showed that temporal lobe and parietal-occipital lobe had great effect in depression identification.