With recent advancement in automation and data acquisition technologies, a number of quality variables are often measured at high frequency and thus are likely to be autocorrelated. The multivariate exponentially weighted moving average (MEWMA) control chart with a scalar smoothing parameter has been widely suggested for monitoring autocorrelated vectors, owing to its simplicity. However, the use of a scalar smoothing parameter cannot take the correlation structure of variables into account, which in turn could deteriorate the detection performance of MEWMA control charts. Motivated by this, we generalize the MEWMA chart for monitoring autocorrelated vectors by using a weight matrix instead of a scalar smoothing parameter. The weight matrix is expected to have non-zero off-diagonal elements in order to make use of the correlation structure of the variables. The comparison results show that the generalized MEWMA chart can outperform the traditional MEWMA chart under a majority of shift directions, although it complicates the chart design to some extent.