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We consider Langevin equation involving fractional Brownian motion with Hurstindex $H\in(0,\frac12)$. Its solution is the fractional Ornstein-Uhlenbeckprocess and with unknown drift parameter $\theta$. We construct the estimatorthat is similar in form to maximum likelihood estimator for Langevin equationwith standard Brownian motion. Observations are discrete in time. It is assumedthat the interval between observations is $n^{-1}$, i.e. tends to zero (highfrequency data) and the number of observations increases to infinity as $n^m$with $m>1$. It is proved that for positive $\theta$ the estimator is stronglyconsistent for any $m>1$ and for negative $\theta$ it is consistent when$m>\frac{1}{2H}$.

Consistency of the drift parameter estimator for the discretized fractional Ornstein-Uhlenbeck process with Hurst index $H\in(0,\frac12)$