The B(E2;↓) value of the neutron-rich nucleus 12Be has been determined through the measurement of the lifetime of the first 2+ state using a modified Doppler-shift attenuation method (DSAM). The first excited state was produced by the inelastic scattering of the intermediate energy 12Be beam off a thick gold target, which played two roles, to excite the beam and to decrease the velocity. The lifetime has been determined to be 2.5±0.7 (stat) ± 0.3 (syst) ps, which gives a B(E2) value of 5.0±1.3±0.5 in Weisskopf units. The result shows a large quadrupole strength in the ground state transition. The B(E2) value together with the deformation length measured by proton inelastic scattering yields a neutron quadrupole matrix element two times larger than those for 14C and 16O.