Zirconium silicate is an extremely durable materials with the variety of useful optical and electronic properties and broad range of existing and potential applications. Using Density Functional Theory (DFT) in local density approximation (LDA) and generalized gradient approximation (GGA) with plane wave (PW) basis set we have revealed eight new polymorphs of ZrSiO4 within the energy range ∼1 eV above the most stable zircon which have higher and lower density than experimentally known zircon and reidite. Two structures, which have both silicon and zirconium atoms six-fold coordinated, orthorhombic AlTaO4-like (alumotantite) and monoclinic PbWO4-like (raspite), have similar energies at GGA level ∼0.35 eV above reidite and density intermediate between zircon and reidite. Among two low-density structures, which can be potentially revealed experimentally in the nanocrystalline thin films, the orthorhombic CaSO4-like form has energy similar to reidite but much lower density. We also conducted a comparative study of existing ZrO2 and SiO2 polymorphs, which demonstrates the higher accuracy of GGA approach.