In view of the problem that the reflected wave curve is complicated when a variable impedance pile is under vertical transient non-free end excitation，we build a simplified mathematical pile-soil vertical vibration model on the basis of the longitudinal vibration theory of one-dimensional viscoelastic rods and the soil plane strain model. We adopt the raised-cosine function to simulate the transient excitation force，obtain a semi-analytical solution to the dynamic response at an arbitrary position on the pile stem through matrix operation and integral transform，and compare with the measured low-strain data about offshore bored piles with long steel casings. The results show that the proposed method demonstrates the characteristics of the reflected signal at the end of the steel casing above the concrete top. Furthermore，combining the above method with the simulation of similar working conditions under design and construction parameters is conducive to analyzing complicated reflected wave curves produced by non-free end excitation applied to variable impedance piles and identifying the pile stem defects.