Architected Cement-based Materials (ACMs) are a class of cement-based materials whose internal geometry is architected at mm-cm scale to achieve desired or unusual mechanical properties. Designing the complex internal structure of ACMs is challenging and often relies on experimentally guided trial-and-error approaches. No systematic design method of ACMs has been developed to date. This paper presents a novel framework for simulation and learning-driven design of ACMs. Two design approaches are proposed: random generative design and reinforcement learning-driven design. For the former approach, an integrated simulation framework that generates a large number of random ACM designs, converts them into finite element meshes, and evaluates their performance by nonlinear structural analysis was developed. In the learning-driven approach, a generate-and-test algorithm was developed in which the ACM design is evolved through iterative simulations based on a reinforcement learning technique coupled with a deep learning algorithm. To study the applicability of the proposed framework, ACMs with high specific energy absorption under compression were designed by using the two design methods. The possible macroscopic-property space and the characteristic features of extreme cases could be systematically estimated from the simulation results of the generative design approach. The learning-driven approach could identify high-performance ACM designs more efficiently. In addition, experimental validation was conducted and the predicted high energy absorption capability of ACMs could be confirmed. Therefore, it has been demonstrated that the proposed framework is promising for systematic design of ACMs and extending the range of mechanical properties achievable by cement-based materials.