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‎In this paper‎, ‎in order to establish a confidence interval (general and shortest) for quantiles of normal distribution in the case of one population‎, ‎we present a pivotal quantity that has non-central t distribution‎. ‎In the case of two independent normal populations‎, ‎we construct a confidence interval for the difference quantiles based on the generalized pivotal quantity and introduce a simple method for extracting its percentiles‎, ‎by which a shorter confidence interval can be constructed‎. ‎We will also examine the performance of the proposed methods by using simulations and examples‎.