In this paper we present the theory, design, and implementation of a continuously tunable phase shifter using a surface-wave structure. The surface-wave travels on a reconfigurable impedance surface which is implemented by arranging dipoles on a single-layer PCB where a varactor is placed in the gap in the middle of each dipole. The proposed phase shifter operates at X-band from 8.5 to 10 GHz and it can provide 464 o phase shift with a figure of merit of 110 o /dB at 9.16 GHz. In the designed phase shifter, the varactor loss is less than all other loss mechanisms which makes it possible to achieve a high figure of merit at a high frequency range. The proposed phase shifter can be used in the design of phased arrays that require a high radiation efficiency at a relatively high frequency compared to the self-resonance frequency of the tunable electronic components.