CH(x) (x=1-3) adsorptions on clean and CO precovered Rh(111) surfaces were studied by density functional theory calculations. It is found that CH(x) (x=1-3) radicals prefer threefold hollow sites on Rh(111) surfaces, and the bond strength between CH(x) and Rh(111) follows the order of CH(3)<CH(2)<CH. A slight attraction between adsorbed CH(x) and CH(x), CH(x) and CO, CO and CO radicals/molecules at coverage of 1/9-1/4 ML is found, and considerable repulsion is built up at coverage higher than 1/4 ML. It is found that CH(x) adsorption results in the reduction of work function due to charge transfer from the adsorbates to the substrate. For CH(3) adsorption, charge accumulation between the substrate and carbon atom is identified, which results in C-H stretch mode softening. For CO precovered surfaces, the mode softening is prevented due to the weakened interaction between CH(x) and substrates from repulsive interaction between adsorbates. Conversely, the overall charge transfer from the CH(x) (x=1-3) to the substrate enhances the charge back donation from the substrate to the empty antibonding states of adsorbed carbon monoxide, which results in the softness of the C-O stretch, respectively. The C 1s surface core-level shifts for CH(x) with and without the presence of CO were calculated, and a negative shift with respect to the carbon in atop CO on Rh(111) is found, and the negative shift follows the order of CO<CH(3)<CH(2)<CH. The results are analyzed in details by difference of charge density and projected density of states.