High crystalline quality ZnBeSe epilayers with different compositions were grown on GaAs substrates by molecular beam epitaxy using Be-Zn co-irradiation of the III-V surface and a ZnSe buffer layer. A (1 x 2) reflection high-energy electron diffraction pattern was formed after the Be-Zn co-irradiation indicating the formation of Be and Zn dimers on the GaAs surface. A two-dimensional growth mode was observed throughout the growth of the ZnSe buffer layer and ZnBeSe epilayer. Narrow X-ray linewidth as low as 23 arcsec with the etch pit density of mid 10(4) cm(-2) were obtained. The linewidth of the dominant excitonic emission is about 2.5 meV at 13 K for the near-lattice-matched ZnBeSe layer. For a nitrogen-doped sample, capacitance-voltage measurements showed a net acceptor concentration of 2.0 x 10(17) cm(-3). In addition, the use of a BeTe buffer layer and of a Zn-irradiation with a ZnSe buffer layer were also investigated.