The hourglass fermion, as an exotic quasiparticle protected by nonsymmorphic symmetry, has excited great research interest recently. However, its bulk counterpart in two-dimensional (2D) solid-state materials has seldom been studied. In this Letter, we propose a 2D rectangular lattice made of p_{x} and p_{y} orbitals with glide mirror symmetry but without inversion symmetry to realize the hourglass fermion. The glide mirror symmetry guarantees a Dirac nodal line, while the Rashba spin-orbital coupling splits it into two Weyl nodal lines and generates two pairs of hourglass fermion located at the glide mirror plane. Furthermore, based on first principles calculations, we predict a surface-supported 2D material Bi/Cl-SiC(111) to realize our proposal, making a huge-bandwidth hourglass cone. Moreover, the hourglass fermion exhibits a spin-momentum locking spin texture and also sustains a giant spin Hall conductivity. Our results demonstrate a general routine for designing an hourglass fermion in 2D materials, which will be easily extended to other surfaces with different adatoms and lattice symmetries.