A high-resolution ultraviolet spectrometer was employed for a measurement of the H Lyman-beta (H L(beta)) emission Doppler line profile at 1025.7 Angstrom from dissociative excitation of H-2 by electron impact. Analysis of the deconvolved line profile reveals the existence of a narrow central peak, less than 30 m Angstrom full width at half maximum (FWHM), and a broad pedestal base about 260 m Angstrom FWHM. Analysis of the red wing of the line profile is complicated by a group of Werner and Lyman rotational lines 160-220 m Angstrom from the line center. Analysis of the blue wing of the line profile gives the kinetic-energy distribution. There are two main kinetic-energy components to the H(3p) distribution: (1) a slow distribution with a peak value near 0 eV from singly excited states, and (2) a fast distribution with a peak contribution near 7 eV from doubly excited states. Using two different techniques, the absolute cross section of H L(beta) is found to be 3.2+/-0.8X10(-19) cm(2) at 100-eV electron impact energy. The experimental cross-section and line-profile results can be compared to previous studies of Ha (6563.7 Angstrom) for principal quantum number n=3 and L(alpha) (1215.7 Angstrom) for n=2.