Carbon-enhanced metal-poor stars (CEMPs) areconsidered to be related to the first generation of stars, and responsible for the chemical evolution of the early galaxy.More than half of them are in binaries, and could be explained by binary evolution, but the formation channel of them is still not fully understood. Of the hundreds of carbon-enhanced metal-poor stars, there are nine carbon-enhanced metal-poor RR Lyrae stars (CEMP-RR Lyrae) have been identified, and at least seven of them are very likely not binaries. The usual binary star evolution channel is difficult to produce such single star, particularly with enrich of carbon. One way in which such a single star might be formed is after the merger of a helium white dwarf with a Hertzsprung star. Weuse a stellar evolution code to calculate models of the remnants of the mergers, and find that the models can reproduce the observed distribution of such carbon-enhanced metal-poor single RR Lyrae stars in terms of their surface temperatures, gravities, and carbon abundances.