Muon scattering imaging technology can be used to detect nuclear material and is of considerable significance in nuclear safety. However, it is difficult to distinguish special nuclear materials from high-Z objects effectively by using the existing muon scattering imaging technologies. Muon-induced neutrons emitted from special nuclear materials can help to identify the existence of special nuclear materials. However, this method has long imaging time and low imaging quality. Multimodal imaging of muon uses both the information about scattering muons penetrating the material and the information about muons stopped by material and generating secondary induced neutrons, which can overcome the shortcomings of single imaging method effectively. The detection model is set up based on Geant4. The simulation programs of muon imaging in coincidence with muon induced neutrons, scattering imaging of muon, and multimodal imaging of muon are developed by using Cosmic-ray Shower Library as particle source, and the imaging algorithms are implemented respectively on the basis of the simulated data. Two imaging models are designed for muon scattering imaging. The first one is a single ²³⁵U cube, and the second one is composed of four cubes, namely ²³⁵U cube, ²³⁹Pu cube, lead cube and aluminum cube. This simulation has completed muon scattering imaging of single cube and four cubes. In the part of muon imaging in coincidence with muon induced neutrons, the neutronic gain of the HEU (90% ²³⁵U) plate, LEU (20% ²³⁵U) plate, and DU (0.2% ²³⁵U) plate, as well as the relationship between the neutronic gain of these three uranium plates and the energy and charged properties of the muon are obtained by simulation, and then two imaging models are set up. The first one is composed of four cubes, namely ²³⁵U cube, ²³⁹Pu cube, lead cube, and aluminum cube, and the other is comprised of multilayer nuclear components. The 2D and 3D reconstruction results of multi-objects and multilayer nuclear components are obtained through muon imaging in coincidence with muon induced neutrons. Then the multimodal imaging of muon for three cubes is realized in the presence or absence of iron shielding shell. The imaging capabilities are compared with the muon scattering imaging capacities and muon imaging capacities in coincidence with muon induced neutrons. Simulation studies indicate that multimodal imaging of muon based on scattering and secondary induced neutrons can effectively combine the advantages of every single imaging method. The multimodal imaging of muon can take advantage of available information more efficiently, which is helpful in improving the imaging quality. Multimodal imaging of muon not only has the advantages of short imaging time and high imaging quality, but also can distinguish special nuclear material from other high-Z materials clearly, which is vital for detecting special nuclear materials.