The bandwidth limitation of optoelectronic devices is a key constraint for realizing higher capacity short-reach optical communication systems. In this work, we show that the performance of the timing recovery algorithm will significantly impact the performance of bandwidth-limited optical PAM-4 signals. To address this problem, we introduce a moving average filter (MAF) into the Gardner retiming loop to realize ultra-stable retiming without any pilot symbols. It enables a significantly reduced timing jitter, especially for bandwidth-limited conditions. Based on simulations, we show that the proposed retiming scheme will give a stable sampling phase, which is beneficial to the performance of the decision feedback equalizer. Compared to the system based on the traditional Gardner timing synchronization algorithm, the 2-dB power budget gain is realized. The proposed method improves the equalization performance of short-reach optical communication systems where complexity and processing latency are important concerns.