Stochastic block models can fit the generation of various networks, mining implicit structures and potential connections within these networks. Thus, they have significant advantages in community detection. General stochastic block (GSB) models discover general communities based on link communities, but they are only applicable to directed non-attributed networks. This study proposes a degree corrected general stochastic block (DCGSB) model for undirected attributed networks which models both network topology information and node attributes. In the DCGSB model, it is assumed that the generation of network topology information and node attributes follows a distribution in the form of power functions. Node degrees are introduced to characterize the scale-free property of networks, which allows the model to better fit the generation of real networks. The expectation-maximization algorithm is employed to estimate the parameters of the DCGSB model, and node-community memberships are obtained by hard partition to complete community detection. Experiments are conducted on three real attributed network datasets containing different network structures, and the proposed model is compared with ten existing community detection algorithms. Results show that the DCGSB model not only inherits the advantages of GSB models in identifying general communities but also outperforms the ten algorithms in community detection due to the introduction of attribute information and node degrees.