We analyze the cross-correlation function between the soft and hard X-rays of atoll source 4U 1735-44 with RXTE data, and find anti-correlated soft and hard time lags of about a hecto-second. In the island state, the observations do not show any obvious correlations, and most observations of the banana branch show a positive correlation. However, anti-correlations are detected in the upper banana branch. These results are different from those of Z-sources (Cyg X-2, GX 5-1), where anti-correlations are detected in the horizontal branch and upper normal branch. In this case, the lag timescales of both this atoll and Z-sources are found to be similar, at a magnitude of several tens to hundreds of seconds. As a comparison, it is noted that anti-correlated lags lasting thousands of seconds have been reported from several black hole candidates in their intermediate states. In addition, for an observation containing four segments that show positive or anti-correlation, we analyze the spectral evolution with the hybrid model. In the observation, the anti-correlation is detected at the highest flux. The fitting results show that the Comptonized component is not the lowest at the highest flux, which suggests that the anti-correlation corresponds to the transition between the soft and hard states. Finally, we compare the corresponding results of atoll source 4U 1735-44 with those observed in Z-sources and black hole candidates, and the possible origins of the anti-correlated time lags are discussed.