This paper considers the problem of monitoring the mean of a normally distributed process variable when the objective is to effectively detect both a sustained shift and a linear drift. The design and application of a generalized likelihood ratio (GLR) chart for simultaneously monitoring a sustained shift and a linear drift are evaluated. The GLR chart has the advantage that when we design this chart, we do not need to specify the size of the parameter change. The performance of the GLR chart is compared with that of other control charts, such as the standard cumulative sum (CUSUM) charts and the cumulative score (CUSCORE) charts. And we compare the proposed GLR chart with the GLR charts designed for monitoring only a sustained shift and for monitoring only a linear drift. Finally, we also compare the proposed GLR chart with the chart combinations. We show that the proposed GLR chart has better overall performance for a wide range of shift sizes and drift rates relative to other control charts, when a special cause produces a sustained shift and/or a linear drift in the process mean.