For the purpose of performing direct continuation of high-precision gravityand magnetic potential field on the three-dimensional irregularly undulateobservational curved surface, this paper puts forward two continuation methodsfor potential field curved surface, i. e. trigonometric function method and evenposition method, which are characterized by high precision, strong adaptabili-ty, high computation speed, negligible error in block processing and easy reali-zation on microcomputer. Tentative calculations on theoretical models andprocessing of practical data prove the correctness and reliability of these twomethods and their softwares.