In this study, pressure losses associated with a core-annular flow (CAF) through three horizontal pipes of 25 mm, 52.7 mm and 80.1 mm in internal diameter are measured. The working fluids for the core-annular flow are two immiscible fluids, highly viscous oil and water. Oils with viscosities of 2.82 Pa⋅s at 20°C and 8.92 Pa⋅s at 20°C are used in the experiment. The oil-water flow rate ratios (ratio of oil flow rate to water flow rate) are set at 2.6, 3.0, 3.4, 4.0 and 4.6 for the pipe of 25 mm in diameter and at 4.0 for the pipes of 52.7 mm and 80.1 mm in diameter. Based on the results of the experiment, a simple model for the pressure loss of a core-annular flow is derived. This model is used to estimate pressure losses of core-annular flows at various flow rate ratios and pipe diameters. To validate the model, the pressure loss data from the experiment are compared with those of the model. The comparison shows that this model is useful for predicting pressure loss of a CAF when oil does not wet the pipe wall extensively. In addition, it is observed in the experiment that pressure loss of CAF with the two viscous liquids is slightly higher than that of single-phase water. This indicates that pressure loss of a CAF is largely independent of oil viscosity.