A novel background calibration technique for timing mismatch in time-interleaved ADCs (TI ADCs) with fast convergence speed is presented in this brief. The proposed calibration applies a customized neural network (NN) to extract the information of timing skews for compensation. Compared to the conventional background methods for calibrating timing mismatches without reference, this work significantly increases the convergence speed with high accuracy. In comparison with prior NN-based calibration works, this work could follow the error changes in the background and has stronger robustness, also without any risk of fidelity problem. A 12-bit 3GSps 4-channel TI ADC model with noise and jitter is simulated for verifying the effectiveness of this technique. Simulation results show that the proposed technique could improve the SNDR and SFDR by 7.41dB and 24.73dB respectively, with only 1536 samples for convergence. Off-chip validation with a 12-bit 3GSps 4-channel TI ADC also proves the effectiveness and practicality of this brief.