Resistivity and magnetic susceptibility measurements under external pressure were performed on NaFe 1−x Co x As (x = 0, 0.01, 0.028, 0.075 and 0.109) single crystals. For both underdoped and optimally doped NaFe 1−x Co x As, the maximum T c reached as high as 31 K under certain pressures. Meanwhile the overdoped sample with x = 0.075 also exhibits a positive pressure effect on T c , and an enhancement of T c by 13 K is achieved under a pressure of 2.3 GPa. All of these superconducting samples show large positive pressure coefficients on superconductivity, being distinct from those of Ba(Fe 1−x Co x ) 2 As 2 . However, the superconductivity cannot be induced by pressure in heavily overdoped nonsuperconducting NaFe 0.891 Co 0.109 As. These studies reveal that the electronic structure is very different between superconducting and heavily overdoped non-superconducting NaFe 1−x Co x As, consistent with the observation of angleresolved photoemission spectroscopy.