Understanding the generation and evolution of magnetic fields in high-energy-density plasmas is a major scientific challenge in broad research areas including astrophysics, cosmology, and laser fusion energy. However, the fully three-dimensional (3D) topologies of such dynamic magnetic fields are still unknown yet. Here we report experiments of the first 3D synchronous proton radiography for self-generated magnetic fields in respectively laser-produced low-Z CH and high-Z Cu plasmas. The radiography images show that abundant 3D filamentary structures of magnetic fields grow up in coronal region of CH plasmas, while for Cu, the fields are majorly compressed along the dense surface region whose internal structures are pretty vague. These results are reproduced and explained by a combination of radiation-magnetohydrodynamic, particle-in-cell and Vlasov-Fokker-Planck simulations, where the cross-scale effects of Biermann battery, Nernst advection, resistive diffusion, Righi-Leduc and particularly kinetic Weibel instability are all taken into account. Our findings provide much enlightenment to the role of magnetic field generation in implosion and hohlraum dynamics of laser fusion.