We formed the first ``atomic-optics'' beam of electron-spin-polarized hydrogen atoms using a quasiparabolic polished copper mirror coated with a hydrogen-atom-reflecting film of superfluid $^{4}\mathrm{He}$. The mirror was located in the gradient of an 8-T solenoidal magnetic field and mounted on an ultracold cell at 350 mK. After the focusing by the mirror surface, the beam was again focused with a sextupole magnet. The mirror, which was especially designed for operation in the magnetic field gradient of our solenoid, increased the focused beam intensity by a factor of about 7.5.