Partial Least Squares Regression (PLSR) is a linear regression technique developed as an incomplete or "partial" version of the least squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. Robust methods are introduced to reduce or remove the effects of outlying data points. In the previous studies it has been showed that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS1 algorithm (PLSR with univariate response variable) becomes unnecessary. Therefore, we propose a new robust PLSR method based on robustification of the covariance matrix used in classical PLS1 algorithm. We select a reweighted estimator of covariance, in which the Minimum Covariance Determinant as initial estimator is used, with weights adaptively computed from the data. We compare this new robust PLSR method with classical PLSR and four other well-known robust PLSR methods. Both simulation results and the analysis of a real data set show the effectiveness and robustness of the new proposed robust PLSR method.