In this paper, a new estimator combined estimator (CE) is proposed for estimating the finite population mean (Y)over-bar(N) in simple random sampling assuming a long-tailed symmetric super-population model. The efficiency and robustness properties of the CE is compared with the widely used and well-known estimators of the finite population mean (Y)over-bar(N) by Monte Carlo simulation. The parameter estimators considered in this study are the classical least squares estimator, trimmed mean, winsorized mean, trimmed L-mean, modified maximum-likelihood estimator, Huber estimator (W24) and the non-parametric Hodges-Lehmann estimator. The mean square error criteria are used to compare the performance of the estimators. We show that the CE is overall more efficient than the other estimators. The CE is also shown to be more robust for estimating the finite population mean (Y)over-bar(N), since it is insensitive to outliers and to misspecification of the distribution. We give a real life example.