To improve the water stability of copper-based metal-organic framework materials (HKUST-1) for the selective adsorption of organic solvents and oil phases in oil-water mixtures, hydrophobic modification of HKUST-1 crystals with stearic acid (SA), which has a long carbon chain structure, was used as a modifier to prepare hydrophobic/lipophilic HKUST-1@SA crystals. The chemical structure, microscopic morphology, thermal stability, water stability and wettability of the crystals before and after modification were characterized by FTIR, XRD, SEM, TGA and contact angle analysis. The selective adsorption oil phase performance of HKUST-1@SA was tested through oil-water separation, oil absorption performance and recycling experiments. The mechanism of hydrophobic modification and oil-water separation has also been suggested from a molecular perspective. The results showed that the hydrophobically modified HKUST-1@SA crystals reacted at 90 °C for 2 h using a 1.5% stearic acid-ethanol solution, the water contact angle on the surface of the hydrophobically modified HKUST-1@SA crystals was 135° and the oil contact angle was 0°. The water contact angle of the HKUST-1@SA crystals remained at 120.4° at 300 °C, and there was no obvious change in crystal structure and wettability after being exposed to water for 14 days. The crystals showed some thermal and water stability. The adsorption amounts of HKUST-1@SA crystals on crude oil, gasoline, kerosene, diesel oil, and n-hexane were 5.54, 8.11, 7.68, 7.22, and 8.32 g/g, respectively. Treatment at 250 °C removed adsorbed light oils (gasoline, hexane) from inside the crystals. After repeating the adsorption-desorption 20 times, the attenuation of the n-hexane adsorption amount was less than 10.2%. The long-chain alkyl groups provided by stearic acid significantly improved the water stability of HKUST-1@SA crystals and enabled them to selectively adsorb tiny oil droplets in the aqueous phase.