Wavelength-tunable optical vortices with a topological charge equal to l=1 of orbital angular momentum (OAM) were experimentally realized using a single off-axis spiral phase mirror (OSPM) with lasers of various visible-light wavelengths. Using an OSPM designed for 561 nm and an incidence angle of 45°, circular doughnut-shaped l=1 optical vortices were obtained at 561, 473, and 660 nm by rotating the OSPM to modify the laser incidence angle. Wavelength-tunable l=1 optical vortices were obtained at the respective incidence angles of 45°, 53.4°, and 33.7°, because the effective geometrical thickness of the OSPM, which determines the order of OAM, was identical at each wavelength. This flexible OSPM which operates over a wide wavelength range will provide continuously wavelength-tunable optical vortices for applications in the fields of advanced optics and photonics in which optical vortices with wide wavelength tunability are in demand.