We perform simulation study for a 10-kg ^{100}Mo-based bolometeric demonstration experiment for neutrinoless double-beta decay (0nu beta beta ) search at China JinPing underground Laboratory (CJPL). Cosmogenic production of radionuclides in ^{100}Mo-enriched lithium molybdate crystals and copper components of the detector system are studied using Geant4 toolkit based on the simulated cosmic ray data from the CRY library. Background energy spectra of the cosmogenic radionuclides including ^{56}Co, ^{82}Rb and ^{88}Y which are harmful for the ^{100}Mo-based 0nu beta beta experiment are investigated. We then evaluate the total cosmogenic background level in the ^{100}Mo 0nu beta beta search energy region of interest (ROI) for the demonstration experiment. After one year of cooling down underground, the residual background contribution is found to be 1.8 times 10^{-6} cts/kg/keV/yr and 3.3times 10^{-4} cts/kg/keV/yr from crystals and copper components, respectively. Furthermore, underground cosmogenic activation of copper and lithium molybdate crystal is calculated based on the simulation spectra of neutron and proton in CJPL. The underground cosmogenic background is found to be negligible in the ROI.