Abstract: Based on the concept of the element energy projection (EEP) and the fix-end method, which makes a priori quantitative error estimation in finite element method (FEM) possible for boundary value problems (BVP), it extends the technique to a typical initial value problem (IVP), i.e., the motion equation. Taking the linear element with single degree of freedom as example, the possibility of a priori quantitative error estimation is discussed by using Taylor series expansion without the needs for FEM solution, which in turn achieves a priori determination of adaptive step-size for the linear time-element. Some preliminary examples are given to show the feasibility and effectiveness of the proposed method.