Biomimetic oil-infused surfaces promise great potential in water and energy applications, such as condensation processes. Surface micro/nano-structures facilitate the oil infusion and therefore enhance the water condensate mobility. In this work, we fabricate micro-grooves on surfaces and coat them with nanoparticles to strengthen the oil infusion. We demonstrate directional transport and spontaneous removal of condensing droplets can be achieved with diverging micro-grooved channels. Condensate droplets on the channel walls would submerge into the microgrooves owing to the capillary pressure gradient in the infusing oil. The submerged and confined droplets deform and exhibit a difference between the back and front curvatures, which makes the droplets move along the channel diverging direction. These nano-porous groove surfaces possess the ability to uniformly spread the infusing oil and minimize its drainage. The surface oil-infusion performance is experimentally evaluated by studying the impact of surface structure dimensions and intrinsic wettability on oil drainage. Our findings on spontaneous condensate removal offer great opportunities in enhancing condensation heat transfer.