The torque and velocity profile of a flow between two coaxial cylinders with a highly water-repellent wall were measured experimentally. Two kinds of highly repellent wall were tested to clarify the surface condition effect of the cylinder on laminar drag reduction with fluid slip. The results of torque measurement showed that laminar drag reduction does not occur for a highly water-repellent wall with no fine grooves at the wall surface. Fluid slip of Newtonian fluids was clarified by measuring the velocity profile close to the highly water-repellent wall in a Couette flow by a tracer method for flow visualization. The maximum slip velocity is less than 20% of the wall velocity of the rotating inner cylinder. The result of the drag reduction ratio for the torque was calculated by applying to the slip velocity, and agrees with the experimental result quantitatively. Consequently, the gas trapped in the fine grooves plays an important role in laminar drag reduction with respect to fluid slip. From the flow visualization of laminar Taylor–Couette flow, the intervals of Taylor cells become slightly irregular in the case of the cylinder with a highly water-repellent wall. The calculation result for the Taylor cell applying the fluid slip boundary condition agrees with the experimental result.