The quality of smooth blasting including the volume of over-/underbreak and blasting-induced damage of surrounding rocks has been extensively considered to be highly correlated to both the cost and advancement rate of rock tunnelling excavated by the drill-blast method. A general control strategy for smooth blasting is too difficult to be available due to the uncertainties and complexity of rock masses, as well as the varying blasting operations. As prerequisite for the evaluation of the blasting quality, effective identification of the influential factors affecting smooth blasting usually plays a significant role in the improvement of smooth blasting design. Compared to the expensive and time-consuming experiments including physical modelling and field tests, numerical modelling, as a cost-efficient approach, offers an attractive alternative to investigate the influential factors in terms of weight, which might be more applicable and reliable for the optimization of smooth blasting parameters. In this case, the dominant factors and secondary factors can be quantitatively identified. Considering the dominant factors often orient the development of things; in this work, a numerical-based approach was proposed to quantitatively identify the dominant factors influencing the quality of smooth blasting. Proposed 3-dimensional blasting modelling was based on LS-DYNA to simulate the occurrence of smooth blasting in rock masses, and the erosion algorithm was also employed to determine the fracturing of jointed rocks. The orthogonal experimental design method was utilized to optimize the experimental arrangement. Seven factors with 4 levels including the perimeter hole spacing, line of least resistance, charge concentration, charging explosive, type of rock mass, detonation velocity, and drilling deviation were taken into account. The geological setting and project background of a real rock tunnel served for the Chengdu-Chongqing high-speed railway were selected as the site conditions to perform the numerical investigation. Calculated area and distance of overbreak as the observed parameters indicating the quality of smooth blasting were utilized to determine sensitivities of factors based on the range analysis of orthogonal experiments. The results suggested that the type of rock mass has the greatest influence on the blasting quality, whereas the charge concentration and detonation velocity can be considered as the secondary factors under the specific site conditions. The proposed numerical approach for assessing influential factors of quality of smooth blasting under specified geological conditions is expected to improve the parameter design and operation of smooth blasting in practical applications.