In the context of radio galaxy classification, most state-of-the-art neural network algorithms have been focused on single survey data. The question of whether these trained algorithms have cross-survey identification ability or can be adapted to develop classification networks for future surveys is still unclear. One possible solution to address this issue is transfer learning, which re-uses elements of existing machine learning models with different applications. Here we present radio galaxy classification based on a 13-layer Deep Convolutional Neural Network (DCNN) using transfer learning methods between different radio surveys. We find that our machine learning models trained from a random initialization achieve accuracies comparable to those found elsewhere in the literature. When using transfer learning methods, we find that inheriting model weights pre-trained on FIRST images can boost model performance when re-training on lower resolution NVSS data, but that inheriting pre-trained model weights from NVSS and re-training on FIRST data impairs the performance of the classifier. We consider the implication of these results for future radio surveys being planned for next-generation radio telescopes such as ASKAP, MeerKAT, and SKA1-MID.