In this study, I address the testing problem on the regression trend slope in cointegrating regressions when the stochastic regressors have nonzero drifts. A test statistic constructed using demeaned integrated modified ordinary least squares (IMOLS) residuals is considered. Asymptotic theory for the test is developed under the standard small-b framework, resorting to the consistency of heteroskedasticity and autocorrelation consistent (HAC) estimator. The simulation experiment shows the proposed test performs reasonably compared to the existing fully modified OLS-based test in Hansen (1992b).