Recently supramolecular hydrogels have become a hot research point in the field of hydrogels. As promising building block for supramolecular hydrogel, DNA has received considerable attention for its designability and excellent mechanical strength, and DNA hydrogel has shown great potential applications in biological and medical areas. To better understand the structure and property of DNA hydrogel, computational simulation is a very powerful tool to complement experimental study. However, owing to the large size of DNA hydrogel system and long time scale of self-assembly process, it is practically unachievable to simulate the system directly at an all-atom level. Coarse-grained simulations should be developed. In this article, we propose a highly coarse-grained model to investigate the mesoscopic structure of well-designed pure DNA hydrogel constructed by Y-shape DNA blocks and linear DNA linkers with sticky ends. In this model, we ignore almost all the atomic details of the building blocks and only give a coarse-grained description of their shapes, and carefully design the Lennard-Jones (LJ) interaction between coarse-grained particles in order to take into account the fact that any of the three arms of a Y block can only interact with a single linker (i.e., the bond is saturated). To design a suitable interaction, here we use a combination of LJ repulsive potential between like particles and LJ attracting potential between unlike particles. Our simulation results show that the hydrogel has two states, namely, homogeneous liquid-like state at high temperature and spongy gel-like state at low temperature. State of this system is related to the degree of cross-linking which is described by average cross-linking pair number per Y-scaffold here. We find that the pair number per Y-scaffold is positively correlated with the concentration of hydrogel blocks, which is consistent with experimental results. We also investigate the distribution of local structure by using voronoi cells, then predict the hole size of the hydrogel network. By the micro-rheology method, we then determine more precisely the value of the transition temperature to be 0.06/kB-0.10/kB, which is also consistent with experimental result. The quantitative relation between transition temperature and binding energy of sticky ends can hopefully provide guidance for the optimal design of DNA hydrogels. The qualitative and even semi-quantitative agreement between our simulation results and experimental results indicates that our coarse-grained model is a suitable and effective one for this pure DNA hydrogel system. The basic ideas of our model can be generalized to more complicated DNA hydrogel systems.