This paper presents a new confidence interval for a coefficient of variation of a normal distribution. The proposed confidence interval is constructed by adjusting the constant number in Vangel’s [9] confidence interval. Monte Carlo simulations are used to investigate the behavior of this new confidence interval compared to the existing confidence intervals based on their coverage probabilities and expected lengths. Simulation results have shown that all cases of the new confidence interval have desired minimum coverage probabilities of 0.95 and 0.90. Moreover, this new one is better than the existing confidence intervals in terms of the expected length for all sample sizes and parameter values considered in this paper.