This paper presents the measurement of the relative width difference ΔΓd/Γd of the B0-B¯¯¯¯0 system using the data collected by the ATLAS experiment at the LHC in pp collisions at s√=7 TeV and s√=8 TeV and corresponding to an integrated luminosity of 25.2 fb−1. The value of ΔΓd/Γd is obtained by comparing the decay-time distributions of B0 → J/ψKS and B0 → J/ψK*0(892) decays. The result is ΔΓd/Γd = (−0.1±1.1 (stat.)± 0.9 (syst.)) × 10−2. Currently, this is the most precise single measurement of ΔΓd/Γd. It agrees with the Standard Model prediction and the measurements by other experiments.