The high-yield synthesis of network-like branched silicon nitride (Si3N4) nanostructures by a simple template catalyst-assisted pyrolysis of a polymer precursor, perhydropolysilazane, was reported. The templates were silicon wafers deposited with Fe films of 5-20 nm in thickness. The processes simply involved thermal cross-linking of the preceramic polymer, crushing of the solidified polymer chunks into fine powder, and thermal pyrolysis of the powder under flowing high-purity nitrogen. The collected white network-like branched nanostructures are alpha-Si3N4 of hexagonal phase, and their microstructures, in which the diameters of each linear part of the network-like nanostructure varied in a very wide range from tens of nanometers to hundreds of nanometers, strongly depend on the applied growth parameters, where the key factors are the heating rate and catalyst thickness for change in the diameters. It was proposed that the Si3N4 nanonetworks were formed through "metal-absorption on the surface of nanostructures" model by vapor-liquid-solid mechanism. The reaction mechanism of Si3N4 nanonetworks was also discussed.