Solar radio bursts can be used to study the properties of solar activities and the underlying coronal conditions on the basis of the present understanding of their emission mechanisms. With the construction of observational instruments, around the world, a vast volume of solar radio observational data has been obtained. Manual classifications of these data require significant efforts and human labor in addition to necessary expertise in the field. Misclassifications are unavoidable due to subjective judgments of various types of radio bursts and strong radio interference in some events. It is therefore timely and demanding to develop techniques of auto-classification or recognition of solar radio bursts. The latest advances in deep learning technology provide an opportunity along this line of research. In this study, we develop a deep convolutional generative adversarial network model with conditional information (C-DCGAN) to auto-classify various types of solar radio bursts, using the solar radio spectral data from the Culgoora Observatory (1995, 2015) and the Learmonth Observatory (2001, 2019), in the metric decametric wavelengths. The technique generates pseudo images based on available data inputs, by modifying the layers of the generator and discriminator of the deep convolutional generative adversarial network. It is demonstrated that the C-DCGAN method can reach a high-level accuracy of auto-recognition of various types of solar radio bursts. And the issue caused by inadequate numbers of data samples and the consequent over-fitting issue has been partly resolved.