  The paper deals with the regression model $X_t = \theta t + B_t$, $t\in[0, T
]$, where $B=\{B_t, t\geq 0\}$ is a centered Gaussian process with stationary
increments. We study the estimation of the unknown parameter $\theta$ and
establish the formula for the likelihood function in terms of a solution to an
integral equation. Then we find the maximum likelihood estimator and prove its
strong consistency. The results obtained generalize the known results for
fractional and mixed fractional Brownian motion.
