Smart meters (SMs) are an important part of smart power grid, and they are also the basis for power grid operation control and trade settlement between power supply and electricity consumption. The measurement results are directly related to the security of power grid and whether the trade settlement between both sides is fair and reasonable. Therefore, it is very necessary and meaningful to carry out the detection of out-of-tolerance errors in the operation of meters. Through analyzing the data from advanced metering infrastructure (AMI) and utilizing multiple linear regression techniques, in this paper we provide a detection method for electric smart meters anomaly with error tolerance based on Tikhonov regularization and generalized cross-validation (GCV) optimization in distribution network of tree topology. To verify the effectiveness and practicality, the method proposed is applied in the actual distribution area. The results show that the proposed method did not need to calculate the network loss independently in advance, and it can find out the smart meters with error tolerance accurately.