Structural properties of normal-type spinel ZnCr2Se4 have been studied as a function of temperature by means of neutron diffraction. It is found that the structural phase transition (T-C) from a cubic to orthorhombic symmetry simultaneously occurs at the antiferromagnetic phase transition temperature (T-N similar to 21 K), where the cubic and orthorhombic symmetry is O-7(h)-Fd3m and D-24(2h)-Fddd, respectively. The structural phase transition is mainly characterized by the cooperative displacements of Se2- ions, which are induced by a magnetostriction resulting from the magnetic interaction of Cr3+ ions in CrSe4 chains along [110]. The antiferromagnetic magnetic structure below TN is made by a spiral magnetic coupling between the ferromagnetic CrSe4 chains around crystallographic screw axes, which are parallel to an orthorhombic C axis. The spiral long-range order of the spins of Cr3+ is incommensurate and its periodicity of q along a reciprocal lattice axis C* shows temperature dependence from about 0.47 (2.5 K) to 0.43 (18 K). The spiral periodicity of the spin order along the C axis shows a first order transition at about 21 K.