Cross sections of the e + e − annihilation into one photon plus two vector mesons, such as J/ψρ, J/ψφ, and ρφ at the center of mass energy √ s = 10.58 GeV are calculated. These shed light on the measurement of the e + e − annihilation cross section via radiative return in B-factories. At another center of mass energy √ s = 3.097 GeV, namely the J/ψ resonance peak, the processes e + e − → γV V and e + e − → γγV (with V being ρ, ω, or φ) are calculated with similar method. These calculations give estimation of the background levels in the study of radiative or double radiative decays of J/ψ.