Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG)in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency ωc and an exteal laser field of frequency ωL.It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency ωO,the frequencies of the cavity mode ωc and the vibrational mode v.It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.