The lattice shell structure is widely adopted in large-span spatial structures (LSSSs). Under impact load, the steel column supports have a great impact on the working performance of the lattice shell structure. To ensure the impact resistance of the structure, this paper establishes a finite-element model of a single-layer latticed shell with steel column supports, and applies the model to analyze the nonlinear dynamic response of the latticed shell structure under the lateral impact from a heavy vehicle. In addition, the authors examined the influence of three factors, namely, peak impact load, lateral stiffness of support and number of impact points, over the latticed shell structure under the said impact. The results show that: except for the impacted support and rods connected to the support, the entire latticed shell structure is basically in an elastic state. Overall, the working performance of the latticed shell structure is not damaged by the impact load, that is, the structure still enjoys satisfactory strength and stability, with no dynamic instability. Hence, the latticed shell structure boats good working performance under impact load.