The fracture processes in concrete can be simulated by lattice fracture model [1]. A lattice network is usually constructed on top of the material structure of concrete, and then the mechanical properties of lattice elements are assigned, corresponding with the phases they represent. The material structure of concrete can be obtained experimentally by X-ray computed tomography. Alternatively it is also possible to simulate a virtual material structure of concrete. A simple way to represent the material structure of concrete is to put multiple spheres in a matrix, where the spheres are interpreted as aggregates. This assumption of the shape of aggregates might have influences on the fracture processes in concrete, such as the microcracks propagation path. Recently the Anm material model was proposed and implemented, which can produce a material structure of concrete with irregular shape aggregates [2]. The irregular shape is represented by a series of spherical harmonic coefficients. The method to determine these spherical harmonic coefficients from aggregate shapes was elaborated in [3]. The further mechanical performance evaluation would benefit from this more realistic material structure. In this paper a material structure of concrete is simulated by the Anm material model. A number of irregular shape particles are planted in a matrix. This material structure is then converted into a voxelized image. Afterwards a random lattice mesh is made, and three types of lattice elements are defined, which represent aggregates, matrix and interface respectively. A uniaxial tensile test is set up and simulated by fixing all the lattice nodes at the bottom of the specimen and imposing a prescribed unit displacement onto all the nodes at the top. The lattice fracture analysis gives the stress-strain response and microcracks propagation, from which some mechanical properties such as Young's modulus, tensile strength and fracture energy can be predicted.