This paper presents a time series model whose OLS estimator is asymptotically efficient regardless of singularity of its limiting sample covariance matrix. In the literature on stationary time series analysis, the classical result of Grenander and Rosenblatt (1957) has been used to judge asymptotic efficiency of the regression coefficients on deterministic regressors that satisfy so-called Grenander's condition. Without the condition, however, it is not obvious that the model is efficient. In this paper, we introduce such model by proving the efficiency of the model with a slowly varying (SV) regressor. This kind of regressors is known to appear asymptotic singularity in the sample moment matrix (see Phillips (2007)), so that Grenander's condition fails. The contribution of the present paper is that we reveal the existence of asymptotically efficient model that does not satisfy Grenander's condition.