Vulnerability analysis is significant for the security of LTE public networks and private networks. The current research on LTE vulnerability considers little about the balance between effectiveness and complexity of jamming. This paper analyzes the vulnerability of LTE initial synchronization mechanism, and puts forward a LTE jamming method based on spoofing synchronization signals to verify this vulnerability. By changing the correlation peaks' positions of initial synchronization with the spoofing signals, the method can make synchronization fail. Simulation results verify the effectiveness of this method, prove the vulnerability of the initial synchronization mechanism and also reveal the optimal time shifting between the spoofing signals and the actual signals.