This paper attempts to describe the dynamics of population change in Taiwan since 1905. It is found that the population growth during the past seventy years has effected cyclical shifts in the age composition of the population. Before the war, the age composition shifted toward the young end with the proportion of young surviving children enlarged. Then after the war, the age composition shifted back to the old end indicating the shrinkage of the proportion. It is suggested that the changes in age composition can be attributed to the trend of mortality decline since the early twenties. In other words, we argue that the mortality decline had a larger effect on the surviving of young children than the other age groups. With a controlled population model proposed by Ronald D. Lee, we show that the fertility decline, which effected in the upward turnning of the age composition after the war, is simply a response to the mortality decline with a time lag of about twenty years.