Deep Convolutional Neural Networks (CNNs) have been widely used in image classification tasks, but the process of designing CNN architectures is very complex, so Neural Architecture Search (NAS), automatically searching for optimal CNN architectures, has attracted more and more research interests. However, the computational cost of NAS is often too high to apply NAS on real-life applications. In this paper, an efficient particle swarm optimisation method named EPSOCNN is proposed to evolve CNN architectures inspired by the idea of transfer learning. EPSOCNN successfully reduces the computation cost by minimising the search space to a single block and utilising a small subset of the training set to evaluate CNNs during evolutionary process. Meanwhile, EPSOCNN also keeps very competitive classification accuracy by stacking the evolved block multiple times to fit the whole dataset. The proposed EPSOCNN algorithm is evaluated on CIFAR-10 dataset and compared with 13 peer competitors comprised of deep CNNs crafted by hand, learned by reinforcement learning methods and evolved by evolutionary computation approaches, which shows very promising results by outperforming all of the peer competitors with regard to the classification accuracy, number of parameters and the computational cost.