Multi-path fading seriously affects the accuracy of timing synchronization (TS) in orthogonal frequency division multiplexing (OFDM) systems. To tackle this issue, we propose a convolutional neural network (CNN)-based TS scheme assisted by initial path acquisition in this paper. Specifically, the classic cross-correlation method is first employed to estimate a coarse timing offset and capture an initial path, which shrinks the TS search region. Then, a one-dimensional (1-D) CNN is developed to optimize the TS of OFDM systems. Due to the narrowed search region of TS, the CNN-based TS effectively locates the accurate TS point and inspires us to construct a lightweight network in terms of computational complexity and online running time. Compared with the compressed sensing-based TS method and extreme learning machine-based TS method, simulation results show that the proposed method can effectively improve the TS performance with the reduced computational complexity and online running time. Besides, the proposed TS method presents robustness against the variant parameters of multi-path fading channels.