  In this paper, we study a model which is composed by the cosmological
constant and dark matter with nonzero equation of state parameter, which could
be called as $\Lambda$wDM. In the synchronous gauge, we obtain the perturbation
equations of dark matter, and deduce the evolution equations of growth factor
about the dark matter and baryons. Based on the Markov Chain Monte Carlo
method, we constrain this model by the recently available cosmic observations
which include cosmic microwave background radiation, baryon acoustic
oscillation, type Ia supernovae, and $f\sigma_8(z)$ data points from
redshift-space distortion. The results present a tighter constraint on the
model than the case without $f\sigma_8(z)$ data. In 3$\sigma$ regions, we find
the dark matter equation of state parameter $w_{dm}$=$0.000111_{-
0.000701-0.00137-0.00180}^{+0.000688+0.00136+0.00181}$. After an extra model
parameter $w_{dm}$ is considered, the difference between the minimum values of
$\chi^2$ of our model and standard model is $\Delta\chi^2_{min}=0.598$.
Although the currently available cosmic observations mildly favor the nonzero
dark matter equation of state parameter, no significant deviation from the
$\Lambda$CDM model is found in 1$\sigma$ region.
