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Tree growth in mountain ecosystems is affected by complex environments, and its relationship with climatic and environmental factors varying with elevation. In order to examine the spatial variation and temporal stability of the growth/climate relationship of <i>Betula platyphylla</i> (<i>BP</i>), the dendrochronological method was used to analyze the radial growth/climate relationship between 1946 and 2016 of the <i>BP</i> trees along an altitudinal gradient in the Changbai Mountain of northeast China. Our results showed that the mean sensitivity of <i>BP</i> was higher than that of other species studied in Changbai Mountain. The growth/climate relationship of <i>BP</i> trees varies with altitude, and this conclusion has reached a consensus from the study of tree growth response to climate change. More specifically, at low altitudes (550–995 m a.s.l.), the radial growth of <i>BP</i> is mainly affected by spring precipitation and temperature in May and October of the current year. However, at high-altitude areas (1210–1425 m a.s.l.), it is mainly affected by the temperature in September of the previous year and May of the current year. Furthermore, the growth/climate relationship of <i>BP</i> trees showed temporal instability. After 1970, the rise in temperature inhibited the growth of <i>BP</i> at low altitudes and promoted the growth of <i>BP</i> trees at high altitudes. In the context of continued warming in the future, the white birch stands in Changbai Mountain will move to higher altitudes.