We describe an extreme-ultraviolet (EUV) polarimeter that employs laser-generated high-order harmonics as the light source. The polarimeter is designed to characterize materials and thin films for use with EUV light. Laser high harmonics are highly directional with easily rotatable linear polarization, not typically available with other EUV sources. The harmonics have good wavelength coverage, potentially spanning the entire EUV from a few to a hundred nanometers. Our instrument is configured to measure reflectances from 14 to 30 nm and has approximately 180 spectral resolution (lambda/Delta lambda). The reflection from a sample surface can be measured over a continuous range of incident angles (5 degrees-75 degrees). A secondary 14 cm gas cell attenuates the harmonics in a controlled way to keep signals within the linear dynamic range of the detector, comprised of a microchannel plate coupled to a phosphorous screen and charge coupled device camera. The harmonics are produced using approximately 10 mJ, approximately 35 fs, and approximately 800 nm laser pulses with a repetition rate of 10 Hz. Per-shot energy monitoring of the laser discriminates against fluctuations. The polarimeter reflectance data agree well with data obtained at the Advanced Light Source Synchrotron (Beamline 6.3.2).