The dynamic response of the lining structure of an existing tunnel during the blasting construction of a new tunnel is studied based on the Bogongao No.1 tunnel project which belongs to one of the level 1 risk tunnels of Ganzhou-Shenzhen high-speed railway. The numerical model of the test section is established by using ANSYS/LSDYNA finite element software. By comparing the field measured with the model calculated vibration velocities, the reliability of the numerical simulation is verified with the inversed surrounding rock mass parameters. Furthermore, based on the parameters of the test section, a numerical model of the intersection of the two tunnels is further constructed, which is used to analyze the vibration attenuation law of the existing tunnel lining structure in the intersection, and put forward vibration reduction measures under the worst cases at the intersection. According to the research results, the largest vibration velocity appears at the vault of the existing tunnel and the smallest vibration velocity is at the floor. Within 30 m from the front and back of the intersection, the vibration velocity at the vault is about 2.0~2.3 times that at the side wall closer to the blast. For the whole section of the existing tunnel, the controlled vibration velocity of 1.6 cm/s. However, for the side wall, the early warning value of vibration velocity should be 0.8 cm/s. When the cut holes are bottom initiated, most of the explosion energy is transmitted to the unexcavated area, which contributes to a higher attenuation rate of vibration velocity from the excavated area of the new tunnel than from the unexcavated area. The blasting scheme of the test section is no longer applicable to the cross affected section. On the premise of considering both the work efficiency and blasting effect, the vibration velocity of the secondary lining in the existing tunnel can be controlled within the safe range after the footage is shortened to 1.0 m and the cut hole charge is reduced to 9.86 kg.