A method for automatically controlling drilling weight-on-bit for using a drill-string to drill along a wellbore includes establishing a drill-string model and a wellbore model, wherein the drill-string has a plurality of components along the length thereof, and the wellbore has a plurality of sections. A surface tension data of the drill-string can be acquired, and a friction coefficient-depth distribution can be obtained by calibrating the surface tension data in the drill-string model and wellbore model, and the drilling weight-on-bit can be predicted according to the calibrated drill-string and wellbore models.