We consider a Pseudo-Poisson process, when the leading Poisson
process has a random intensity. Under an appropriate distribution for the random intensity the corresponding Pseudo-Poisson process possesses a covariance of the fractional Ornstein-Uhlenbeck process. Applying to the Pseudo-Poisson processes with the considered random intensity the Lamperti transform and then the Central Limit Theorem for vectors we obtain the fractional Brownian motion as a limit in a sense of weak convergence of finite dimensional distributions.