Time and frequency synchronization is very critical in LTE downlink. This paper proposed a joint time and frequency synchronization algorithm to estimate the carrier frequency offset (CFO), including the integer frequency offset (IFO) and the fractional frequency offset (FFO), and the start position of a radio frame. The FFO is first estimated by maximum likelihood auto-correlation algorithm. After the FFO compensation, the received signal is cross-correlated with the nine possible primary synchronization signals (PSS) in time domain to obtain the start position and the IFO. Simulation results show that the performance of the proposed synchronization algorithm is more robust than the traditional algorithms especially in large CFO.