The initial synchronization problem for third Generation Partner Project(3GPP) Long Term Evolution(LTE) downlinks is studied, when there is a large Carrier Frequency Offset(CFO) between the base station and a mobile terminal working at a low Signal to Noise Ratio(SNR). A robust initial synchronization algorithm is proposed in detecting the Primary Synchronization Channel(P-SCH) sequence after the Integer Frequency Offset(IFO) compensation. Simulation results demonstrate that the proposed algorithm can achieve high detection probability for the P-SCH sequence and low Mean Square Error(MSE) of the CFO estimation at low SNR regions.