The Fermilab muon g-2 experiment plans to use the existing BNL E821 muon strorage ring and constructs a new detector system to measure the anomalous magnetic moment of the muons to a precision of 0.14ppm, a fourfold improvement over the previous Brookhaven E821 experiment. The muon anomaly is a fundamental physics quantity, which can be precisely measured and accurately computed within the Standard Model and a comparison of experiment to theory is a sensitive test of the completeness of the theory. The current comparison to the accepted theory shows a deviation of more than 3 standard deviations, which might be an indication of New Physics beyond the Standard Model.