Using the ERA-interim reanalysis data of ECMWF as the reference, numerical errors of the GRAPES global model are evaluated first. A numerical correction of the systematic model errors is then performed based on the historical observation data by using the Anomaly Numerical-correction with Observations (ANO) method. The effect of the ANO on the global forecast is tested by several case studies, and significant improvements on the global forecasting quality are confirmed. The ANO application in numerical results from 15 to 24 July during 1984-2014 shows significant positive effects in the circulation forecasts compared to those without the ANO application. For example, the potential height and temperature forecasts have been improved in various regions. Analysis of the geopotential height forecasts at 200 hPa shows that the anomalous correlation coefficient (ACC) increases by 0.05 and the root mean square error (RMSE) decreases by 12 gpm on average for all the 31 cases. Similar results can be found at other levels. The above results verify the validity of the ANO method in the improvement of 10-day numerical weather forecasting skill of the GRAPE global model. Compared with the MOS method, the ANO method is more efficient and maneuverable for application in the operational forecast.