Neural architecture search (NAS) has attracted considerable interest due to its capability of automatically designing effective network architectures tailored to specific tasks. However, most existing NAS methods require extensive computational resources for architecture evaluation. Meanwhile, the increasing demand for deploying deep neural networks on mobile devices highlights the importance of reducing the model size. To overcome the aforementioned challenges, this paper proposes an evolutionary multi-objective NAS algorithm with efficient blocks using training-free ZiCo-Block evaluation, called EZB-NAS. We design two computationally efficient blocks and construct a hierarchical and variable-length search space to discover lightweight architectures. In addition, we improve the ZiCo proxy to reduce the structural bias in block evaluation by averaging the ZiCo scores across all layers within a block. The developed zero-cost proxy, named ZiCo-Block, is integrated into an evolutionary computation approach for lightweight architecture design. With improved genetic operators, we simultaneously optimize the ZiCo-Block score and the number of parameters to discover highly accurate and lightweight architectures. Experimental results on the CIFAR datasets show that EZB-NAS achieves competitive performance in terms of accuracy, model size, and computational cost, compared to efficient NAS algorithms. The source code is available at https://github.com/wangyule0/EZB-NAS .