This article uses arc-length parameters for path planning to carry out robotic fibre placement (RFP) over open-contoured structures. This allows representing the initial path and offset points using an identical mathematical equation and computation by more simple arithmetic. With the help of classical differential geometry, the calculation of fiber-placing paths may be reduced to solution of ini-tial-value problems of first-order ordinary differential equations in the parametric domain (parametrically defined mould surface) or in 3D space (an implicitly defined mould surface), thereby significantly improving on the existing methods. Compared with the conven-tional methods, the proposed method, besides its computational simplicity, has a better error control mechanism in computing the initial path and offset points. Numerical experiments are also carried out to demonstrate the feasibility of the new method in composite forming processes and also its potential application in computer numerical control (CNC) machining, surface trim, and other industrial practices.