Several control charts have been constructed to simultaneously monitor the process mean and variability. A single chart is often used instead of two charts to detect shift in the process mean and variability separately. A new single generally weighted moving average control chart is now proposed to monitor the process mean and dispersion simultaneously, based on Taguchi’s loss function. A Monte Carlo simulation is used to calculate average run length to study the performance of this control chart when the process is shifted. A comparison is made with an exponentially weighted moving average control chart in terms of average run lengths. Two examples are also included for showing the practical application of the proposed control chart.