Numerical modeling of fracture processes of brittle materials, such as cement paste, mortar, concrete and rocks, started in the late 1960s when the discrete and smeared cracking models were introduced. In the 1990s, Schlangen and van Mier proposed another numerical model to compensate the drawbacks of the discrete and smeared cracking models, which is called lattice fracture model. From then on, plenty of investigations were conducted to exploit various applications of lattice fracture analysis, and this contribution is one of them. This paper studies the fracture process of cement paste at microscale, especially the tensile strength, elastic modulus and cracking due to external mechanical loads. The study is based on the microstructure of hardening cement paste and attempts to reveal the relationship between the microstructure and its global performance. Moreover, the crack propagation during the fracture process is also investigated in detail. In this paper, the microstructure of hydrating cement paste is simulated by HYMOSTRUC3D first, and then it is converted into a voxel based image. In the next step, a lattice network is created and the local mechanical properties are mapped from the simulated microstructure. After that, the fracture process is simulated using lattice analysis to obtain the load-displacement diagram and crack propagation. A series of numerical experiments are carried out to illustrate the influences of various input parameters, for instance, the degree of hydration, the Blaine value of cement and the water/cement ratio.