A unit root test based on the modified least squares (MLS) estimator for first-order autoregressive process is proposed and compared with unit root tests based on the ordinary least squares (OLS), the weighted symmetric (WS) and the modified weighted symmetric (MWS) estimators. The percentiles of the null distributions of the unit root test are also reported. The empirical probabilities of type I error and powers of the unit root tests were estimated via Monte Carlo simulation. The simulation results showed that all unit root tests can control the probability of type I error for all situations. The empirical power of the test is higher than the other unit root tests, and Apart from that, the and tests also provide the highest empirical power. As an illustration, the monthly series of U.S. nominal interest rates on three-month treasury bills is analyzed.