To examine subcritical accretion disks, we performed two-dimensional axisymmetric calculations by solving a set of fully non-linear hydrodynamic equations coupled with radiation transport. Focusing on the accretion disks of neutron stars near to the Eddington luminosity LE, we obtained thermally stable accretion disks where the radiation pressure and electron scattering are dominant. The thermally stable disks are interpreted in terms of the slim accretion-disk theory. While the accretion disks are unstable to convection and convective cells generally stretch from the disk mid-plane to the disk surface in the inner disk. It has been found that convection is an important energy-transfer mechanism along the vertical direction of the disk. A very rarefied, hot, and optically thin region is formed along the rotational axis of the disk. The relativistic jet with a collimation angle of less than 10 degrees is generated in the rarefied optically thin region, mainly due to the dominant radiation-pressure force. The results of subcritical accretion onto a neutron star are discussed in relation to SS 433.