The single-particle trajectories of relativistic electrons are studied in a magnetic field con-figuration consisting of a uniform axial guide field and a helical periodic wiggler field. The steady-state trajectories and the first order perturbed trajectories are analysed carefully. Based on the numerical simulations about the experiments which have been made at Shanghai Institute of Optics and Fine Mechanics, the effect of the betatron oscillations due to the transverse varing of wiggler field is first shown in the case that there is a axial guide field. In this case the betatron oscillations equations are drived. Its period and the relation between phase in X dirction and in Y dirction are obtioned. Further more, numerical simulations are made. The results of analytical calculation are in good agreement with the numerical simulations.