To perform a complete scan of a small diameter pipe is difficult for two reasons. First, the beam directivity of the Lamb wave within a small diameter pipe is worse than that within a large diameter pipe. Second, the circumferential range of the small diameter pipe is so limited that it can allow less transducer to be attached on its surface. That means the signals from various circumferential positions are difficult to obtain. This article reports a method that can scan damage within a small diameter pipe using a partially covered axially magnetized magnetostrictive patch transducer (AM-MPT) around the circumference of a pipe based on the analysis of the beam directivity of the MHz Lamb wave. The partially covered AM-MPT was moved around the circumference of a pipe for subsequent measurements to get signals from various circumferential positions. To trigger strong enough MHz Lamb wave, the circumferential coverage of the partially covered AM-MPT was not less than half of the circumference of the pipe, and the greater length-to-width ratio of the magnetostrictive patch was used. The analytical model of beam directivity of the Lamb wave was used to study the Lamb wave propagation in the rolled plate. Then the analytical model was modulated to evaluate the damage scan within a small diameter pipe. The experimental results supported the analytical model through different circumferential coverages of the transducer, and different sizes and axial positions of the damage. The proposed method was proven to have the potential to be applied to damage scans within a small diameter pipe.