Application of pressures or electron-doping through Co substitution into Fe sites transforms the itinerant antiferromagnet BaFe(2)As(2) into a superconductor with the Tc exceeding 20K. We carried out systematic transport measurements of BaFe(2-x)Co(x)As(2) superconductors in pressures up to 2.5GPa, and elucidate the interplay between the effects of electron-doping and pressures. For the underdoped sample with nominal composition x = 0.08, application of pressure strongly suppresses a magnetic

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... stability while enhancing Tc by nearly a factor of two from 11K to 21K. In contrast, the optimally doped x=0.20 sample shows very little enhancement of Tc=22K under applied pressure. Our results strongly suggest that the proximity to a magnetic instability is the key to the mechanism of superconductivity in iron-pnictides.