Beam position monitors (BPMs) are important instruments even in the case of an X-ray free-electron laser (XFEL). Pohang Accelerator Laboratory (PAL) finished the construction of an XFEL (PAL-XFEL) in 2015, and new stripline BPMs were installed in PAL-XFEL. New BPMs were designed to have a strong signal and a high resolution. In addition, the impedance matching was considered to reduce a signal reflection. These features of the BPM design were confirmed with a simulation study as well. Fabricated BPMs were tested by using a wire test stand. Two-dimensional position errors and offsets were measured to select best BPMs for PAL-XFEL. Finally, a real beam test was tried to check the BPM performance and a better resolution than the requirement was obtained.