Time synchronization is essential in multicarrier systems such as filtered orthogonal frequency division multiplexing (F-OFDM) because it determines the whole system’s performance. Differ with OFDM, where subcarrier allocation is not flexible. In F-OFDM, the subcarrier allocation is more flexible, and the whole subcarrier in one symbol can be grouped into several subbands. The use of subcarriers that are limited to only one subband can reduce the performance of time synchronization based on autocorrelation (AC) methods. In this study, we first compare the performance of the AC-based time synchronization algorithms used in F-OFDM when training symbols are limited to one subband. Secondly, we made improvements to the AC-based time synchronization with the averaging technique of its timing metric, thus increasing the accuracy of time estimates in the F-OFDM system. The averaging technique of the timing metric improved the performance of the AC method in cases where the training symbol is limited to one subband, as shown in the simulation results.