Whistler-mode wave-electron interactions constitute an important physical mechanism in the Earth's magnetosphere and the radiation belts of the magnetized planets. From linear theory, an analytical result for the growth rate of electromagnetic R-mode (whistler-mode) waves in a relativistic bi-Maxwellian plasma with given temperature anisotropy is obtained. In order to test the linear theory, a one-dimensional self-consistent electromagnetic particle simulation is performed with a newly developed fully relativistic code. A major background component of isotropic cold electrons and a minor component of anisotropic hot electrons in a uniform magnetic field are assumed. Driven by the temperature anisotropy of the hot relativistic electrons, the whistler-mode waves grow initially linearly, and then nonlinearly to a level at which saturation takes place. Saturation occurs due to a combination of nonlinear trapping of resonant electrons and quasilinear relaxation of the temperature anisotropy. The initial wave growth rate obtained from the particle simulation agrees well with the growth rate predicted from linear theory. In order to reduce electrostatic fluctuations and achieve accuracy in the simulation, a large number of superparticles must be used. (C) 2004 American Institute of Physics.