Using a variational procedure, we have studied the electric field effect on the electronic states in a spherical GaAs-Ga1-xAlxAs quantum dot with parabolic confinement in the case of both finite and infinite barrier heights. For single-particle states of electrons and heavy holes a relative weak Stark shift at weak fields and a transition to a stronger shift at higher fields is found. Compared with a spherical quantum dot with a rectangular confinement potential, the parabolic quantum dot presents a greater restriction to the carriers. As a result, the confinement energy is larger, while the electric field effects on the energy levels are weaker. We conclude that a spherical quantum dot with a parabolic confinement may be significant for practical application.