The partial least squares (PLS) regression is a statistical learning technique which solves the problems of collinearity and/or high-dimensionality in the space of covariates. In this paper, we propose a new estimator for the covariance matrix of the estimator of the regression coefficients in the multivariate PLS model. This new estimator is simple to be calculated and with a low computational cost. We conduct a Monte Carlo simulation study to assess the performance of our proposed estimator. Then, we apply our results to analyze a multivariate real chemical data set. These numerical results show the good performance of our proposal.