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In order to study the influence of blasting construction of rock mass with discontinuities on adjacent tunnels, a feasible blasting scheme is formulated to ensure the safety of adjacent tunnels during construction. Based on the water resources allocation project in the Pearl River Delta, a tunnel construction model is established by using continuous-discontinuous medium mechanics calculation model, Distinct Lattice Spring Model (DLSM), to simulate the impact of blasting construction of the left tunnel on the right adjacent tunnel. According to the numerical simulation results, the stress wave transmission process of the left tunnel with blasting time t = 18 ms is analyzed. Furthermore, the effects of the positions of the discontinuity, the width of the discontinuity, and the angle between the discontinuity and the horizontal direction on the adjacent tunnel are studied. The modelling results show that the existence of discontinuities plays a certain role in improving the safety of adjacent tunnels in the blasting stage. The farther the distance between the discontinuity and the adjacent tunnel is, the smaller the impact of blasting on the adjacent tunnel is. In the process of blasting, the larger the width of discontinuity is, the more effective it is to block the influence of blasting stress wave on the adjacent tunnel. The smaller the angle between discontinuity and horizontal direction, the smaller the impact of blasting on adjacent tunnels.