In consideration of quantization of centre-of-mass motion, we derive the second-order solution of the dynamic equation of a ∧-configuration three-level atom confined in an approximately harmonic trap by using the timedependent perturbation theory. It is found that there are a series of dark lines in the second-order probability spectrum with multi-peak structures, which is the result of the quantum interference from the same vacuum mode in the spontaneous decay process of the trapped atom from the upper level to the two nearby lower levels. Our study shows that the second-order spectrum may be modified by the oscillation frequency Ω of the trap and the frequency difference △ between two lower levels of the three-level atom, and the depth of the dark lines from the vacuum-induced quantum interference effect is strongly dependent on the above two parameters (Ω and △).