Barrel-shaped surfaces are widely used in industries, e.g., blades, vases, and tabular parts. Because a part such as an aero-engine blade is typically quite large, the efficiency of its measurement becomes a critical issue. The recently emerged five-axis sweep scanning technology offers to be a powerful means to significantly increase the efficiency of measurement. However, currently it still mostly relies on humans to manually plan a five-axis sweep scanning path, and in most cases, the surface is simply divided into a number of smaller open patches for which the sweep scanning is then individually planned. We present an algorithm for automatically planning the five-axis sweep scanning for an arbitrary barrel-shaped surface in the form of either a compound, a trimmed, or a simple surface. The planning algorithm is novel in that no partitioning of the surface is needed and a single continuous five-axis sweep scanning path will be generated for the entire surface. By eliminating the nonsweeping time spent by the stylus due to its air-moves between multiple patches and also the time-costly approach-retraction operations required for each patch, the proposed algorithm is able to significantly reduce the total inspection time, sometimes more than 50%, as validated in our physical inspection experiments.