For oscillating heat pipes (OHPs) with low turn number (<9) positioned in the horizontal direction, the working fluid could not easily flow back to the evaporator due to the absence of gravity. Based on this, copper OHP with superhydrophilic micro-/nanostructured surface was investigated to enhance the heat transfer performance by introducing additional capillary force. OHPs with six turns were fabricated with bare copper and micro-/nanostructured inner surfaces for comparison. Pure water was used as the working fluid. Contact angles of water on the copper and superhydrophilic surfaces were 36.7 and 0 deg, respectively. The filling ratios of water were 50%, 65%, and 80%, respectively. Thermal resistance and liquid slug oscillations of OHPs were investigated at the heat input ranging from 100 to 380 W. Experimental results showed that OHPs with the superhydrophilic micro-/nanostructured surface showed an enhanced heat transfer performance due to the micro-/nanostructure-induced capillary flow in the horizontal direction. The optimum filling ratio was 65% in this work. The superhydrophilic micro-/nanostructured surface could significantly facilitate the backflow of the working fluid to the evaporator section and accelerate oscillating motions of liquid slugs. With the increasing of 0–70% in slug oscillating amplitude and 0–100% in slug oscillating velocity, micro-/nanostructured OHPs improved the heat transfer performance by up to 10% compared with the copper OHPs due to the wicking effect.