In this work, we have discovered the anisotropic near-zero thermal expansion (NZTE) behavior in a family of compounds REAgxGa4-x (RE = La-Nd, Sm, Eu, and Yb). The compounds adopt the CeAl2Ga2 structure type and were obtained as single crystals in high yield by metal flux growth technique using gallium as active flux. Temperature dependent single crystal X-ray diffraction suggests that all the compounds exhibit near zero thermal expansion along c direction in the temperature range of 100-450 K. Temperature-dependent X-ray absorption near-edge spectroscopic study confirmed ZTE behavior is due to the geometrical features associated within the crystal structure. The anisotropic NZTE behavior was further established by anisotropic magnetic measurements on selected single crystals. The atomic displacement parameters, apparent bond lengths, bond angles, and structural distortion with respect to the temperature reveal that geometric features associated with the structural distortion cause the anisotropic NZTE along c-direction. The preliminary magnetic studies suggest all the compounds are paramagnetic at room temperature except LaAgGa3. Electrical resistivity study reveals that compounds from this series are metallic in nature.