Evolution of the Hubble parameter In the lambda-CDM model describing an accelerating Universe, the Hubble parameter is currently decreasing with time. Will it continue to decrease forever?
The solution to the Friedmann equation in a flat universe is
$$H^2 = \frac{8\pi G}{3}\rho + \frac{\Lambda}{3},$$
where $\rho$ is the matter density (including dark matter) and $\Lambda$ is the cosmological constant.

As the universe expands, $\rho$ of course decreases, but $\Lambda$ remains constant.

Thus the Hubble "constant" actually decreases from its current value $H_0$ and asymptotically tends towards $ H = \sqrt{\Lambda/3}$ as time tends towards infinity.

As $\Lambda = 3H_0^{2} \Omega_\Lambda$, and measurements suggest that $\Omega_{\Lambda} \simeq 2/3$, then $\Lambda \simeq 2H_0^2$, and the Hubble parameter will therefore decrease to approximately $\sqrt{2/3}$ of its present value if the cosmological constant stays constant.

Of course if $\Lambda = \Lambda(t)$, (ie not the basic $\Lambda$-CDM model) then the behaviour will be different.

EDIT: Another useful form of the solution (for the case of a constant vacuum energy density) is

$$H^2 = H_0^2 \left(  \frac{\Omega_r}{a^4} + \frac{\Omega_M}{a^3} + \frac{\Omega_k}{a^2} + \Omega_{\Lambda}\right),$$
where $H_0$ is the Hubble parameter now, $a(t)$ is the scale factor of the universe, $\Omega_r$ is the current (i.e. $a=1$) ratio of the radiation density to the critical density and $\Omega_M$, $\Omega_k$ and $\Omega_{\Lambda}$ are the equivalent densities for the matter (baryonic and dark), curvature and (constant) vacuum energy densities.

As $a$ increases you can see that all three of the leading terms get smaller and the Hubble parameter decreases at all times. When $a$ is very large, $H$ approaches $\sqrt{\Omega_{\Lambda}} H_0$ as before.