Exclusive ρ+ρ- production in two-photon collisions between a quasi-real photon, γ, and a mid-virtuality photon, γ*, is studied with data collected at LEP at centre-of-mass energies 183 GeV≤√s≤209 GeV with a total integrated luminosity of 684.8 pb-1. The cross section of the γγ *→ρ+ρ- process is determined as a function of the photon virtuality, Q2, and the two-photon centre-of-mass energy, Wγγ, in the kinematic region: 0.2 GeV 2≤Q2≤0.85 GeV2 and 1.1 GeV≤W γγ≤3 GeV. These results, together with previous L3 measurements of ρ0ρ0 and ρ+ρ - production, allow a study of the γγ *→ρρ process over the Q2-region 0.2 GeV 2≤Q2≤30 GeV2. © 2005 Published by Elsevier B.V.