We have developed a method for high precision magnesium isotope measurements in olivine using laser ablation multi-collector inductively coupled plasma mass spectrometry (LA-MC-ICP-MS). The uncertainties of Mg isotopic measurements are 0.071, 0.042 and 0.030‰ (2 standard deviations, 2 SD) for δ26Mg, δ25Mg and δ 26Mg*, respectively, an improvement in precision by a factor of 3 to an order of magnitude over previous reports using similar technique. The precision now is comparable to that of the solution sampling method. To fully exploit the high precision capability, the relative position between sample and standard needs to be carefully evaluated. An artifact could be induced at the level of ∼0.1 ± 0.1‰ range if the samples and standards are too far apart in a large volume sample cell. The Mg isotopic compositions of three terrestrial olivine and two pallasite olivine samples are shown to be identical to that of San Carlos olivine standard within analytical uncertainties. We found no detectable radiogenic 26Mg in the pallasite and chondrule olivines.