Because composite laminates are very susceptible to impact loading even at low velocity, low-velocity impact is an important subject in laminated composite analysis. The impact-induced damage is usually invisible to the naked eye and can cause serious structural degradation. Many low-velocity impact tests were performed in previous studies; however, most were phenomenological analysis. In an effort to further understand the responses of composite laminates under low-velocity impact and to develop an accurate and efficient quantitative simulation in the future, this study was aimed at performing instrumented impact tests and computer simulations. A commonly used computer code—LS-DYNA3D—was evaluated in this study, and the results are valuable for future development of a new computer code. In the study, a low-velocity impact event investigated by Sun and Chen with an indentation law and verified by experiments was used to justify the finite element model and contact parameters. Once the computational scheme was established, it was used for a broader investigation consisting of composite laminates with various thicknesses, fiber angles, and impact velocities. Computational results revealed that the peak contact force and maximum deflection were strongly affected by the thickness of composite laminates, while the fiber angles investigated seemed to play a less significant role. In addition, it was concluded that because delamination modeling was not included in the LS-DYNA3D, the computer code needed to be modified if it was to be used for accurate impact simulations.